This questions is probably getting more common. 32-bit (x86) started with Windows 95(?). 64-bit (x64) started with Windows XP, but wasn't very popular then; now with Vista and the upcoming Windows 7 x64 is much more available. Most computer hardware that is not over about 3 or more years old likely supports x64, so the hardware usually isn't a problem, the software is the main problem. You might be reading this blog to decide if you should use a x64 or x86 OS, I will share my personal experience so you can make your own best decision.
I have used the x86 version of Windows XP, Vista, and Ubuntu. I have used the x64 version of Vista, Windows 7, and Ubuntu. There was absolutely no more work installing the x64 version instead of the x86 version of either Windows or Ubuntu. I've heard that Windows XP has horrible driver support for the x64 version, but I've never tried the x64 of XP. I have not had any driver problems with Windows Vista x64, Windows 7 x64, or Ubuntu x64. 64-bit versions of Windows will not run 16-bit applications. Those applications are usually outdated and have a newer version available. I've used two different computers with the x64 and x86 and never had any hardware driver issue. The default browser of Windows Vista and 7 is the 32-bit version of Internet Explorer because popular programs (Flash, Java, etc.) do not run on the 64-bit browsers on Windows yet. On Ubuntu the default browser is 64-bit and will run Flash and Java; to install Flash on Ubuntu x64 takes a bit of work and a beta package as I am writing this article. Silverlight runs fine on x86 and x64 of both Windows and Ubuntu. Ubuntu x86 works better with some applications, but the x64 version works with all the applications I've tried. A Linux messaging application called aMSN needs a few packages installed before it can be installed. I favor x64 OSes because they have better performance over x86 ones. Also I have 4 GB of RAM as I write, I've heard x86 OSes only will detect something like 3.7 GB.
My conclusion is I like x64. It depends on what applications you use for your decision. I have had minor problems using x64 that are able to be overcome. If you have over 3 GB of RAM you need 64-bit to use all of it. The future of computers is 64-bit; 32-bit is becoming a thing of the past. Software companies (like Adobe) are what's slowing down the conversion. If you have a few applications that don't run on the 64-bit architecture you have a few choices. The first is dual-booting. Installing both x86 and x64 OSes with an option to boot into the one you need. The second choice is using a virtual machine. I like Microsoft's Virtual PC. It has a simple UI and is easy to learn how to use. There is also Virtual Box that I use on Ubuntu. Both of those are free. I've heard of VMWare, but I don't use it, mainly because most of the versions cost money. Both of those methods I described take quite a bit of extra hard drive space (around 15 GB). You do not need an extra licence to install a second copy of a Windows OS under a virtual machine or dual boot. You will need the install disk that you can likely borrow from a friend or order from Microsoft (I think shipping is about $10, and the disk is free).