Magical Jelly Bean Keyfinder
At a Glance
It's compatible with all versions of Windows and can dig up the keys for your operating system, Office apps, and various other programs. On my machine it found keys not just for Windows XP and Office 2003, but also for Command and Conquer: Generals (best RTS game ever, if you want my opinion).
Keyfinder is fast, free, and incredibly handy. It doesn't even require installation. I recommend it not just for those migrating to new PCs, but for anyone who wants to keep a hardcopy of important product keys.