There used to be problems with 64-bit and compatibility. As recently as 8.04, Firefox was only available in 32-bit. However, at this point, there really aren't very many problems at all, and for the casual user, all of the software available is also available in 64-bit.
It does provide a performance boost, and it's necessary to take advantage of more than 4GB of RAM properly.
I will vouch for this comment. 64-bit works just as well as 32-bit on my computers.