When I was installing Ubuntu GNU/Linux with KDE on my latest desktop purchase, I faced a seemingly agonizing decision between 32-bit and 64-bit. There are all sorts of peripheral arguments over performance, but the main arguments on each side are that 32-bit can only support 4 GB of RAM (not technically true) and that 64-bit has limited application support and is more buggy.
Well, I’m happy to report that all of the supposed caveats of 64-bit GNU/Linux completely failed to materialize. After over a week of heavy usage of 64-bit Ubuntu, and installation of a few hundred applications, I haven’t run across a single problem stemming from my decision to use 64-bit. So I would say the choice of 64-bit is a no-brainer. 64-bit has reached maturity, and all of the supposed problems with it are problems of the past. 64-bit is the future of computing (just like 32-bit was the future of computing back when 16-bit was still common). It’s better to make the switch now than to find yourself a year or two down the line facing a 64-bit reinstallation of a 32-bit system. This choice is pretty much set in stone when you install an operating system; there is no upgrade path. So make the correct choice now.
I should point out that not all processors support 64-bit OSes. The older the processor, the less likely it is to offer 64-bit support. So do your due diligence before you accidentally end up downloading the wrong version of a GNU/Linux distribution ISO.