The Ubuntu desktop download screen has a pair of radio buttons you use to select whether you wish to download the 32-bit or 64-bit version. The 64-bit version is labeled "Not recommended for daily desktop usage." If you have a 64-bit processor, why would you not want to use the 64-bit version of Ubuntu?
Update for 10.10: They've removed the "Not recommended" label from the 64-bit version and added a "Recommended" label to the 32-bit version.
Update for 11.04: Same as 10.10.
Update for 12.04: Still says "Recommended" next to 32-bit version of desktop
Update for 12.10: 32-bit version of desktop is still default, says "recommended"
Update for 13.10: 64-bit version is now the default and 32-bit is labelled "for machines with less than 2GB RAM"