Not well. I'm running Windows 7 Professional on a 64bit machine and the older games work under Windows XP compatibility mode - but Generals and Zero Hour don't work at all. None of the games run directly under Windows 7, so if you don't have access to XP mode you won't be able to play them.
Its a shame, but cannot get the original games to run under Windows 7, with attempts on various online patches and XP compatibility mode. Wasted my money.
Its a shame as I would pay £20 just to be able to run the original C&C: Tiberium Dawn in Windows 7/ Windows 8. All the best games from the past are now just memory, as we cannot run them on modern machines.
I am not sure why you cannot play the original C and C dawn on windows 7. I have just played the whole of Nod flawlessly. There is some colour issue. However, if you go to personalise, then windows classic. Next, open resolution but don't change it. Just minimise it to the try. Then run the game. Solves the pixilated inverted colour issue. I know it is weird but try it. There is also a youtube vid showing how to do it. Also, in case it is why it worked for me, I only installed the first game with covert ops. All FMVs, etc worked fine. Not bugs not crashes. I will update when I play the other games if I get them to work.