Ever wondered how bright is the infrared LED on your remote control? Just get a camcorder, or webcam and point it to the remote control. Press any button on the remote and there it is! You can see the infrared light coming out from it!

Most CCDs used in consumer cameras are sensitive to infrared. You'll also notice that most remotes emit pulses instead of a continuous light beam.

I wonder if it's possible to build an infrared flashlight strong enough to allow your camera to see in total darkness.

It is likely that all CCDs are sensitive to infrared light, though I cannot confirm this. This is one of the reasons why a camcorder will white out heavily when pointing towards the sun, or headlights, even if you're not pointing directly at them; They are both very strong sources of infrared.

Some cameras are fitted with a filter to remove infrared light, and they do not have this problem, but they cannot film in the absence of visible light, either.

Some companies, especially Sony, actually make camcorders with an infrared lamp built in, solely for the purpose of shooting video at night in a relatively non-disruptive manner. Of course, some animals can see further into the infrared range than humans, so depending on who or what you're trying to film, YMMV.