They're almost always in one of these places: (user)\AppData (user)\Saved Games My Documents\(game, publisher, or something with "games" in it)
Ok, but let's say I want to remove the game from my HDD and transfer it to an external HDD. But, I want to keep my saved game Now lets say later on down the road, I want to re-install my game with the game save. If I do keep track like you suggested, can I just add the game save back to the original folder I found it in and it will work just fine?
That will usually work. However, I've found a few cases where making a folder before running the game for the first time will actually cause some serious issues. I'm not sure which games did this (it's been a while), but to be safe I usually run the game once, then quit and copy them over.
As long as the OS is the same, moving the files into the same folder you found them in but on a new hard drive should work fine.
*waits until someone says something funny to quote*