If you need to install the game to run it, then in most cases you can't just install the game to a flashdrive and just pop the flashdrive in on any computer and play, because when the game installs, it writes registry files to the computer, and shortcut links, installs drivers, etc...
However, if you had a big enough flash drive to copy all the info from your game disk onto, as well as enough room to install the game onto the flashdrive, you could install the game everytime you want to play it to the flashdrive (if it's on a new computer each time), and that should work.
If you're talking about a simple flash game or a simple game that can be run without installing (just doesn't require it) then yes, you could run those from the flashdrive too, but if your game requires a disk or comes with one, chances are you can't run the game from your flashdrive without installing first.
By the way, flash drives are getting pretty cheap. 2gigabyte Maxtor flash drives were $5 each at Walmart recently. 4gig were like 10-20.. which isn't bad.