The biggest benefit of 64 bit is the 4 GB RAM bottleneck is removed. Previously if you had 4 GB of Ram and a decent video card, your computer would only read about 3.25 GB.
With 64 bit that limit is removed and go up to something like 16 GB for Home and 198 GB for Professional.
Granted there still isn't much out there that really utilizes that much ram, so for todays games and applications, going from 32-64 bit won't make a huge difference.
HOWEVER, you would be a complete fool to buy a new computer with a 32 bit operating system. It's not truly worth it to upgrade your current computer from 32-64 bit right now since there really isn't much use for it, but 64 bit is slowly becoming the standard, so you want your new computer prepared for it (heck there is no price difference between 32 and 64 bit, Windows 7 contains both in the same package).
Short version: It's not worth it to buy a 64 bit windows to replace your current computer, but if you so happen to get a new computer, definitely go 64 bit.
Edit: I should also say, If you really like Windows 7 over your current OS, 64 bit would just be an added bonus for upgrading. But don't go from Vista 32 or xp 32 to vista 64.
