What chord progressions are cool, of course, is somewhat subjective. However, almost everyone admits that the chord progression "i / VII / VI" (also known as Am - G - F, repeat) gets old very quickly.
For the musically uninitiated, chord progressions are read by simply looking at whether the chord in question is uppercase (major), or lowercase (minor). If it is followed with a +, it is augmented; if it is followed by a D, it is diminished. If it says "sus," it is suspended (second or fourth instead of the third; sus4 is the fourth and sus2 is the second. If it says soley sus it means the fourth usually), and if it is followed by m7, 7, 9, 11, or 13, then add the extra notes. Flats are denoted by b's, and sharps are denoted by #'s.
Lowercase letters represent minor, uppercase represent major, + represents diminished, and ş represents diminished. In Bach figured bass analysis, a superscript 6 represents first inversion, 6/4 is second (sans the /). Other chords are a whole other story :) .
A certain user said I should mention this: IV represents the major four of the scale, V would be the major five, while iv is minor, and v is the minor five, and so on.
Another way to read them is by their scale. For example, in the key of A Minor, A minor would be i, B Diminished would be iiş, and so on.
Chord progressions can be formed by utilizing the circle of fifths: I / IV / viiş / iii / vi / ii / V / I or i / iv / VII (or viiş) / III / VI / iiş / v (or V) / i. By taking segments of these (the first is in minor, the second is in major), one can make a generally pleasing (if mildly boring) basis for a melody.
The second technique is using stepwise progressions: I to ii, vi to V, etc., where one steps to the next chord left and right. Musicians tend to hate this, and I am not sure why, because chord progressions such as the i / VII / vi / V flamenco progression is not only obscenely catchy, but stepwise.
If you are a musician, chances are you know the V chord is called the dominant. The entire point of the dominant is to push the melody back to the I, or "home base". The minor key tends to use V instead of v as well as the major, probably because Bach was a sadist who liked to accidentals (this also causes the minor key to turn harmonic minor). Anyway, what few realize is that the dominants have their own dominants (in fact, so does every other chord, other than augmented and diminished chords). By utilizing this fact, one can create secondary dominants, dominants of other chords. Examples would be: I / IV / V of iii / iii (or I / IV / VII / iii). Notice how playing a secondary dominant changes the musical structure to reflect the iii instead of the I. Many hijinks can ensue by these, such as key modulation, where the entire structure of the song is changed to a NEW I, but those are the basics.
Finally, by adding inversions, chord progressions can be made easier to play, more dramatic, or made certain effects achieved. Basically, root position chords (non-inverted) are strongest, followed by first inversion chords, and so on. Diminished chords are almost always first inversion, while everything else tend to be found in every inversion (except for augmented chords... they are root inversion because they turn into other chords if inverted).
By the way, a fun thing to do is to use the VI of a minor key as a deceptive cadence, a la Enya or many Electronica artists. Also, try adding a major seventh to the deceptive cadence, after a small delay, It is very dramatic. | 
