You May Have 64-bit Already
I've been running 64-bit LINUX for some time (as well as 64-bit Solaris and my Mac is 64-bit, too), and many of my friends and peers are amazed that I sprung for a fancy 64-bit processor. I have to shake my head and tell them that if they've got a fairly current PC (purchased in the last 5 years or so), they probably have a 64-bit CPU, too.
All of the Intel Core (Solo and Duo) processors are 64-bit, which is probably what you'll get if you buy a new machine (including a Mac). Most recent Pentiums and Celerons, too. And the AMD processors have been 64-bit for some time as well.
So, the short note is: yes, you may already have a 64-bit CPU, too.
Sadly, while most consumers may understandably not know that they have it, too many developers don't know that people use it, so much of the software out there is still only available in 32-bit form. Even with Windows, the software giant, it will run 32-bit software through emulation. LINUX and Solaris and Mac can do the same thing. The Mac does it best, because of their universal executable idea, the software deployed has 32-bit and 64-bit available.
There are some benefits to using 64-bit OS, but they're pretty hard to see from sitting at the keyboard; it's not like it gets you twice as fast memory access because 64 is twice as big as 32.
The biggest noticeable benefit is the ability to use more than 4GB of RAM. If you're using a 32-bit OS on a computer with 4GB (or more) of RAM, you might be surprised to notice that your machine recognizes less memory. This is because you can't count higher than 4 billion in a 32-bit integer, and so you can't address more memory than that (without trickery they don't use). That means with your 4GB RAM, you have to remove the RAM that your video card has/uses, leaving your OS with less to use.
And the memory limit isn't simply doubled by going from 32-bit to 64-bit (that happens going from 32-bit to 33-bit addressing). Instead of moving from 4GB to 8GB, moving to 64-bit gives 16EB (that's exabytes, or billions of gigabytes).
It's unlikely that you'll walk into a computer store any time soon that sells a system capable of coming close to having that much RAM. Of course, never say never...