There's another factor that hasn't been mentioned: Firmware compatibility. If you're using an EFI-based computer and booting in EFI mode, it's best to boot an OS that's the same bit depth as the EFI. In the case of every UEFI-based PC I've heard of, that means 64-bit; however, some of the earliest Intel-based Macs use 32-bit EFIs, and I've heard rumors that there are some 32-bit EFI-based PCs, too. Although it's possible to boot a 32-bit kernel on a 64-bit EFI, doing so limits your choices on boot loaders and cuts you off from EFI runtime services, which means that you won't be able to adjust your computer's boot manager entries via the "efibootmgr" utility in Linux. These aren't absolutely crippling limitations, but they're enough of an issue that you should consider them if your computer has EFI firmware. (Most computers sold since mid-2011 support EFI, and some sold before then do, too.)
Others have pointed out other issues of 32- vs. 64-bit computing. IMHO, at the moment the reasons for running 32-bit on a 64-bit system are very limited. Memory is seldom an issue, and the RAM consumption differences aren't all that huge, in my experience. The performance boost from running 64-bit code is noticeable but also not huge. The days of needing to run 32-bit programs because 64-bit versions weren't available are largely past, and if you do run into such problems, it's usually possible to run the 32-bit program from a 64-bit installation.
Thus, on balance I recommend a 64-bit installation unless you've got a specific and compelling reason to go with a 32-bit installation. This recommendation is even stronger if your computer has EFI firmware -- even if you're happy booting in BIOS mode or with the EFI runtime services disabled now, you might want to change later. If you go with a 32-bit installation, that would require re-installing everything, since there's no 32-to-64-bit upgrade path. If you install 64-bit now, switching from a BIOS-mode to an EFI-mode boot is relatively easy.