Actually, it depends on what you're using it for.
If you're using Copyrighted material for your personal benefit (i.e. selling it,) it's a no-no. If you're using copyrighted material in a parodic, educational, or slapping something together for the hell of it with no intent on making money off of it, then it's generally fine.
The hardest hit people are the guys who put up whole episodes and/or complete songs. A Lets Play! video is generally fine, as watching someone play a videogame is nothing like actually playing it.
In other words, go ahead. Or you can direct your friend to one of several Fallout 3 lets play that are already on You Tube.