I usually would recommend using the 64-bit version of Ubuntu (if you have a 64 bit machine of course). I have heard that 64 bit will use significantly more memory. I decided to do a little test for myself using a 32 and 64 bit Ubuntu 7.10 Desktop CDs in the same computer.
All memory values are total as reported by gnome's system monitor. First, after booting. 32: 146.0 Mb 64: 212.9 Mb Difference: 66.9 Mb!
Opening Firefox and OpenOffice.org Writer. 32: 180.8 Mb 64: 275.6 Mb Difference: 94.8 Mb!
Opening a BIG picture (courtesy of http://spacetelescope.org/ ) It's heic0710a.tif btw. About 700 mb picture of a spiral galaxy.
32 Bit, slowly loaded it into memory over the network and then apparently failed silently:
64 Bit had success opening the picture of a galaxy (slowly)!
So.. to 64 bit or not (if memory is the only issue)? My answer has changed. Now I'm going to go with: If you have 768 Mb of memory or greater 64 bit could be for you. If not, please stick with 32 bit for the time being.