I do, because I have a really old Xbox 360, the old launch model PRO with the 20GB HDD, but upgraded since then. Because its old, and has been refurbished once before, if I don't install the games to the HDD, when the game runs my Xbox sounds like an airplane taking off, its that bad that it overpowers the actually TV unless I have it blaring to the point where the neighbors can hear it.
So yea, install all the way, same for the PS3, although for different reasons, the PS3 is painfully slow if I don't... I swear the PS3 has some of the worst load times I have ever seen, of course, depends on the game as well.