New and old doesn't really apply as it's more on a game by game basis, there are loads of old and new games where you can just copy the game over to another computer and it will work, excluding restrictions such as DRM of course. There's no magic bullet or blanket statement as to which games will work like that without a problem. Unless it's something like a game collection within some emulation collection but that's besides the point.
You may just as well copy over whatever game you want to take with and give it a quick test, though I would suggest also looking for and copying any related stuff such as things it might store in "My Documents". Many games unfortunately store stuff all over the place, especially in My Documents within a subfolder, such as "My Documents\Games\etc" or "My Documents\EA Games\etc" or "My Documents\Witcher 2" etc. Copy that over aswell to the appropriate place as it often has saves and settings and sometimes more ridiculously mods and other large or important things. Though fortunately some games are at least sensible in that they will simply recreate the missing settings files they store there. Also searching the system partition (presuming you haven't changed environment variables) for the game's or developer's name might show it storing things in something like "C:\Users\<AccountName>\AppData\Local" (have to love the geniuses who store things all over the place).
If after copying the game's folder and other related stuff over it doesn't work, the problem "might" be that it wants registry entries (or files some genius decided to store in yet another silly location). It is possible to find every single file and registry entry the game/application is using (baring some registry values it's expecting to find if they don't exist) and duplicate it all onto the other PC if you're determined enough but there comes a point when it's just easier to re-install.
Still having said that, if you suspect it requires the registry entries there is one thing worth trying as it doesn't take any effort. Simply search the registry for the games install path (eg: "D:\Games\GameName"). Because along with many of the values it stores in the registry it's install path is obviously often one of them, so finding that you'll probably find some others within the same key. At the least this should find the Uninstall key and entries which often includes version numbers etc. You can export that key and then import it on the other PC.
I don't think there's much point in going into more detail about what and how you could find all the files/entries the game might want as it would be easier to simply reinstall the game well before that point.
