Introduction
This writeup is about war in space - a theme of countless stories and films, usually depicted without any connection to reality. Because of that disconnection, this writeup will begin with the things that are so terribly wrong in popular films about space war, and move from there to a realistic extrapolation of a hypothetical high-tech space war.
In the Films
Problems with Star Wars Fights
Problems with Star Trek Fights
Speculations about real war in space
Distance, Speed and Time Distance is the most important difference in space combat. War on a planet is different, since the distances are measured in kilometres at the most. That means that the unaided eye normally can see the enemy. This isn't the case with space battles. The enemy can only be perceived with technological help. Also, the enormeous distances involved result in delays. That means that if one ship is 20 million km away from an other, that one will see the enemy with a delay of one minute, which makes targeting absolutely impossible, since the enemy could go anywhere within that minute. For example, if the enemy had an acceleration of 10 m/s^2, it could be anywhere within a sphere of r = 36 km, V = 150 km^3. (See below for a more complete discussion of whether this shape is a sphere or a bullet-shape.) These effects are further increased by the fact that space is three-dimensional, which is a challenge to human two-dimensional thinking. It also makes it harder to defend against attacks from all sides and makes blockades very difficult. Since spaceships tend to be pretty fast, short-range weapons would have to be fired by high-precision automated systems. As shokwave writes below, Luke can't hit a spaceship whizzing past with several thousand m/s. (Well, maybe he can, but that's not a technological question.
Weapons Of course the enormous distances play an important role in the question of what weapons would be suitable for a war in space. Surely not artillery. Artillery shells are far too slow and inaccurate to be of any use. No, the most obvious weapon is a nuclear missile. After all, there are no problems with nuclear contamination in space, and the destructive power of nuclear weapons makes sure that nothing of an enemy ship will remain after a missile strikes. Of course, these missiles would be guided. The trouble with those weapons is that they can be shot down. After all, the distances are so extreme that a ship shouldn't have any trouble detecting incoming missiles. Also, their guidance systems might be jammed. Another option would be shrapnel cannon or missiles. If a shell containing billions of little metal splinters were accelerated towards the enemy ship, the shell exploding soon after firing, space would be filled with a hailstorm of high-velocity micrometeors which could tear a ship to pieces. A more feasible variety is a missile that contains these splinters, seeking out the enemy, and detonating while still out of range of the enemy defense guns, releasing the splinters towards the enemy ship. The problem with this type of weapon is whether it's possible to hit anything with a weapon of even this considerable spread, and whether it's possible to accelerate the splinters to a velocity at which they could do harm to a spaceship. Designing such a missile would mean trade-offs between speed (larger burn stage-to-warhead ratio), damage potential (magnitude of the nuclear weapon and the amount of shrapnel carried in the warhead), spread (a smaller spread means a denser hail of shrapnel but a larger chance that that hail misses the enemy entirely) and accuracy (how close the missile goes before it releases the shrapnel - closer means more accuracy but a greater likelihood to be shot down before exploding). Lasers would actually be an option as well, because laser beams move at light speed, which makes exact targetting possible. However, a laser beam capable of actually hurting a ship would consume huge amounts of power and would have to be very focussed, making the area of effect very small. Probably the best way to use a laser would be to cover the approximate location of the enemy with a tight zig-zag. Another problem is that lasers can be stopped by reflective surfaces. Perhaps it is possible to accelerate a small shell to near lightspeed. Such a weapon would do devastating damage and would be relatively easy to aim, like a laser, and like a laser, one would have to fire several shots at the approximate position of the enemy to make sure to hit him. Also, recoil would be a serious problem here. Such a weapon is commonly called a Railgun.
Stealth Even though sensors will likely be very advanced, it is possible to be very stealthy in space. The recipe is simple: emit nothing, reflect nothing. That is entirely possible. If a ship is fitted with a radar-absorbing hull and painted black (like a stealth fighter), then it's already quite hard to detect. The main problem at that point is heat emission and engines. If the engines and other systems that produce lots of heat are turned off, it's pretty much impossible to detect a ship. However, a ship cannot maneuver without showing its position. It can only follow a trajectory dictated by gravity and inertia, which is sufficient if the position of its target can be predicted. Imagine an undetectable nuclear warhead aimed precisely at a planet or space station. On a planet, the nuke would only be noticed when it entered the atmosphere, on a space station even only at the moment it hit. So unpredictability is the best defense in space. If your position can be calculated, you're a sitting duck (meaning very easy to hit), whatever your actual speed. Because of this, planets and space stations are very unsafe places to be. There is, however, one way to detect such an "invisible" ship. In its path it will, at various times, occlude stars. If these occlusions are recorded and correlated, the path of such a weapon can be determined. Because the warhead moves predictably, it can easily be shot down if detected. Because of this such weapons need to be as small as possible, which of course limits the payload.
Planets As already stated in the last paragraph, planets are very vulnerable, because their movements are entirely predictable - even space stations can be moved slightly. They are also easy to hit, being several orders of magnitude larger than space ships or stations. However, planets are impossible to invade. On earth there are currently several million soldiers - therefore, several million troops and equipment would have to be transported through space to the planet. That does sound rather incredible. Still, planetary surfaces can be easily bombed into oblivion with a few nuclear bombs. Therefore, they can also be easily held hostage. The conquerors need never touch the planet's surface - only destroy all anti-space defenses and then demand tribute - or else. Tribute, of course, would have to be compact and lightweight. Art, high-tech devices, medicine, rare elements like uranium 235 and particularily information.
The result of this might be war-fleets wandering about and demanding tribute. Others fleets would perhaps offer their services to protect the planet from such blackmailers. The line between pirate and defender would probably blur around the ambiguous word "protection fee".
War ...is perfectly horrible and rather pointless (except World War II, which was just and glorious and totally morally non-ambiguous), and war in space is doubly so. It is hard to imagine any reason why people would build interplanetary or even interstellar spaceships in order to attack somebody so far away that there couldn't possibly be any benefit from it. However, in order for there to be war in space, there would have to be several colonised planets around - which suggests that space travel would need be easy. So perhaps benefits could be gotten. And there are different reasons for war than benefits like riches or land. Ideological or religious reasons, which can inspire people to start utterly stupid things - like war.
Now about the whole bullet shape versus sphere thing: yitz says that I ignore momentum. Well, I don't. The question of whether the shape a spaceship could be in more resembles a sphere or a bullet is not a question of momentum. (All inertial systems are created equal and from the POV of the spaceship it's standing still at the beginning of the evasion maneuver.) It's simply a question of where the spaceship is pointing at the beginning of the maneuver. If the ship takes half a minute to turn 180 degrees, then in a minute it can go a lot farther in the direction it's already pointing at than into the opposite one. If that is the case then the area of space the ship could be in within one minute is indeed more or less the shape of a bullet. If the ship takes even longer to turn compared to the time available, the bullet becomes more pointy. (If the ship can't turn at all the bullet becomes so pointy it's a straight line beginning at the ship's present position.) But if the time the ship takes to turn is small compared to the time available for the maneuver, then the shape of that space will look spherical.
Actually, what would really interest me is writing a simulator for this, using real physics and approximations of real technology. That way such questions as "Are railguns any good?" or "Is the offensive or the defensive in the advantage, and how much?" could be answered. But I lack technical data about missile speeds and lasers and railguns and stuff, and I have no idea how to model a realistic damage system, nor how the simulation should be displayed and controlled. If you do, /msg me.
I've chosen not to extend the scope of the writeup into the tactical / strategical questions SandThatWasARock and yitz have discussed so well below. I think it's better that this writeup focuses on providing a technical basis upon which to found those discussions.
As for the last part, war is not always stupid. Where would we be now if we hadn't taken Hitler out fifty-some years ago? At some point, people probably thought that war would never make sense between countries on different continents, but we eventually proved them wrong. If we really move into space as a race, you can bet that war will move along with us.
One aspect of space warfare neglected in the previous writeups is that of relativity.
On a strategic level, space warfare would take military theory back several hundred years. In the days of old, fleets of ships were dispatched with their orders in hand. It was difficult to change these orders once the fleet was launched. If space ships manage to travel light-days, light-weeks, or even light-months from their port of origin, communications between command and the fleet will become outdated and virtually useless. Like in times past, fleets will have to play hide and seek to engage each other. However, unlike the old days of naval warfare, it will be much more difficult to seek an enemy fleet in space. At sea, boats are only able to move in a plane, but in space ships can move in three dimensions. While, the area of a circle is determined by the square of its radius, the area of a sphere is determined by the cube of its radius. This means that as the distance traveled by a fleet increases, the probability space of where it can be is much larger than that of a naval fleet's. This will lead to an inability to locate enemies which will make it likely that defense and attack will be simplified. Instead of grand strategies, fleets will proceed in an unimpeded way to their targets of attack. Waiting for them, at the objective, will be a rival fleet that will fight them in orbit. The defending fleet will have the duel role of shooting down ordnance launched at the object of their defense while, at the same time, shooting down enemy ships.
On a tactical scale, relativity would also heavily influence space combat. Ships flying at or away from others at high velocities would exhibit red or blue shift. This could cause the use of radar to fail. The expected return frequency of the radar and the actual could be so different, due to red/blue shift, that the antenna would not pick up the return. Additionally, if the ships were travelling very close to the speed of light, radar would be useless, anyway. By the time the radar return from an enemy ship would be detected, it would already be on top of you. Another neglected component of combat at relativistic speeds would be that of time dilation. Time proceeds more slowly for a ship traveling near the speed of light. Humans and computers on high velocity ships would not have as much time to react the actions of slower moving ships, which would appear to move at a blinding pace.
For the above tactical considerations, space warfare at relativistic speeds would be impractical at best. It is more likely that an attacking fleet would decelerate to non-relativistic speeds before falling upon their objective (With gravity, this would be in a literal sense. Remember, "the enemy"s gate is down."). There they would meet an opposing fleet waiting for them. Also, since it would be difficult or impossible to change objectives once the ships have been launched, strategy would devolve into merely deciding the split of strength between defenses and attacks, without the ability to evolve plans with changing information.
We already have three dimensional warfare both in the air and under the water, so human warfare has already been considering it (that extra dimension) for some time.
Combat wouldn't be based around defending the target of the attack. Such defensive tactics would inevitably be too little, too late. As SandThatWasARock pointed out, the sphere around any point in space has significantly more surface area the further away you get. So, If you had an armada trying to defend a planet, you could create a tighter protective sphere closer to the planet, or a loose one further from the planet. Here is a counter tactic for each:
Fleet versus Fleet battles would be less likely, as a single powerful payload could do a lot of damage and if many such attacks were sent, there would be almost no way to stop it, think thousands of suicide bombers the size of cockroaches only two or three of which would need to succeed for complete destruction. Fleet vs. Fleet would be M.A.D., or close enough.
Defense in general is not so viable an option. The best defense would quickly become an offense, the point to remember is that large enclaves who could develop technology faster would have the greatest advantage, though large enclaves in a future of violent space battle would be highly unlikely as a small enemy could very easily destroy a whole planet, or at least it's life sustaining atmosphere.
Tribal nomadic decentralized fleets would be the most likely lifestyle of survival-minded humans in such a future. Large tribes would cut swaths through galaxies along the lines of the richest resource distribution. Smaller tribes could hide by travelling from one resource-poor system to another, staying away from the larger tribes' potential refueling (of any and all natural resources) sources. They might also be able to follow the larger tribes at a safe distance, living off the scraps. Small tribes might specialize in specific technologies in order to make themselves valuable enough to larger tribes to be carried along.
Such battles would be more often a show of force than the need to implement such force. Large tribes would likely go for a larger weaker response to a threat. Smaller tribes for a smaller stronger response. (The difference between cats and bees, for example. A cat will get a clear distance and hiss at an enemy first, a bee will sting and ask questions later, if it isn't dead.)
What is good for defense is good for offense, stealth would be crucial for both, as well as relatively quick motion. Intelligence is also obviously vital. There would be a natural division of intelligence/sensor drones with mainly defensive capabilities and attack drones with quieter short-range perhaps gravity-based sensors. Large fleets of drones are more likely the combat choice in future space conflict for a number of reasons:
Drones and mines would quickly clog the first inhabited systems before humans became entirely nomadic as large self-replenishing intelligent mine-spheres would be perhaps the only way to safeguard planets early on. Dedicated destroyers intent on a planet's demise could still succeed with enough firepower. Avoidance would be the rule of survival in any space war-influenced future. Energy/Radiation shields or any other new technologies could change the rules but not fundamentally. As long as the environment is an open one and motion equates to security, there will be less incentive to form city-states and sedentary communities.
Basically, space warfare as well as space life would develop very quickly into some strange mutant hybrid of animal herds/packs, tribal warfare, suicide bombing, and microscopic life. It would look similar to the deep sea, with large schools of vessels and swarms of smaller drones heading every which way. The only way to know a war is taking place is the constant explosions while the various larger schools of nomadic ships flee the scene and innumerous beehives worth of drones swarm in every direction and flicker in smaller explosions.
The best source to look at for full 3d warfare models where attacks come without warning from almost any vector at all is either deep sea life or microscopic mono/multicellular life. From which we learn very simple lessons:
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