The 32-bit version works on all PCs, the 64-bit version only works on PCs with a suitable processor. Recommending the 32-bit version is simpler than giving out detailed instructions on how to determine whether your computer supports the 64-bit version.
While Linux itself works just as well in 64-bit mode as in 32-bit mode, most binary-only software out there is distributed in 32-bit executables. While the 64-bit edition of Ubuntu includes some support for 32-bit executables, it doesn't include all the libraries in 32-bit form. Furthermore a few programs get confused if you try to compile or run them on a 64-bit system. Recommending the 32-bit edition makes sense for users who might want to install such third-party programs and might not be able to deal with the problems.
On the other hand, the 32-bit desktop edition installs a kernel which is only able to manage a little less than 4GB of RAM (if this hasn't changed in recent versions) and can only let any single process use 3GB. So if you have 4GB or more of RAM, getting the 64-bit edition is a good idea.
Also, as Marco Ceppi writes, see the same question on Ask Ubuntu.