@MikeMakesRight: You can definitely use the old harddrive if you so wish, but you will definitely need a fresh install of Windows.
You can install windows on the drive without formatting and retain your data. Going from 32 bit to 64 bit will be fine. You will have a lot of junk left over and will have to reinstall your programs, but it will get you going if you are in a pinch. Here is a video of that process that may help you if needed
If it is within your means, buying a new HDD is a good idea for a few reasons. HDD's being mechanical, are ticking time bombs and being that yours is already 3 years old, it can't hurt to replace it (although it is not uncommon for a HDD to last many years so don't be too worried). A new hard drive will also allow you to do a clean install of Windows and keep your current data safe. If you do buy a new hard drive, unplug the old one while doing the new install so you do not accidentally format the wrong drive (if you are new to this sort of thing).
Either way you go, BACK UP YOUR DATA. It can't be stressed enough that backing up your data is important. Today this is a very easy thing to do with things like dropbox or carbonite depending on your storage needs or even burning data to DVD's.
Windows is actually pretty resilient to hardware changes (it's something they've been working on since XP and Win7 is really go at it, shame Linux seems to be totally useless about hardware changes) but the best move is to build a new OS installation (old files will be moved to an archive folder when you do the clean install as long as you don't reformat the drive/tell it to do an update or any other gotcha during the install process so you can copy back the documents and then reinstall the programs (and maybe even copy back settings files for the software if you want to dive into the file structure to grab them and they don't use the registry to lock them to per-installation IDs)) and always remember to back up any files you want to keep.
For anyone who does want to do an in-place hardware swap, I would say that downloading the driver installer for the mobo (with network drivers) is critical as Windows sometimes doesn't have a generic driver and being stuck the other side of an update with a working system but no working networking to download a the driver is a pain. And while you're doing that you might as well download the latest drivers for everything to make life easier. Then try and uninstall any drivers you know you'll not be using when the system reboots, power down and upgrade, and then see what Windows does during the next boot (it sometimes goes into a safe-mode type boot to deal with the hardware changes) and hopefully it comes back.
The brand of motherboard shouldn't really matter, the best bet is to install generic drivers for the chipset (so an Intel P35 (random example) motherboard you can get the ASUS or Gigabtye branded driver package or so straight to Intel and get the drivers they make for that chipset) just like you do for graphics cards, it the person who designs the silicon you should talk to about drivers is possible, not the guy who stuck the chip on a PCB and sold it in the shop. I've never tried going from Intel to AMD on the same Windows7 installations, but I have been able to let Win7 boot and update from P35/P45/H57/Z68 (which share some similarities and driver support, which may be why Win7 can boot far enough to detect the changes and continue with an in-place upgrade/driver reinstall) and obviously I don't install a new OS just to change from AMD to nVidia or vice versa so that process has always been designed to cope with a generic driver for the initial boot period before card specific drivers are required.
As noted, you can certainly install "over top" of your old installation, and Windows will move your old files into an archive for later use.
As Shivoa pointed out, you *can* technically do a harddrive swap into a new machine, but I don't recommend this for any sort of long-term OS use: method is nice for when you're trying to boot some else's harddrive in your machine temporarily - it is not meant to replace a regular installation. A fresh install will give you a nice, clean starting point with a nice, clean registry/driver library. Old fragments can come back to haunt you from old installations. while it can be done, it is, in my experience, going to give you more headache than it's worth. I had some stronger wording in my original post that basically said that it is impossible to do - but it's not... it's just not worth it, in my opinion.
You're best to install over your old windows installation if you're not buying a new drive. If you are buying a new drive, you can install to the new drive and then use your second drive for extra storage. In fact, the file system should still be intact, so once you get your new installation set up, you can drag and drop files from your old harddrive.
Also, if you don't uninstall your old drivers before hand, switching card brands greatly reduces your chance of a successful boot. Hell, even if the cards are the same brand but different generation, there is no guarantee that you won't bluescreen. Graphic card drivers are the worst when it comes to compatibility.
After reading all of your comments, I have decided that the easiest thing for me to do is to abandon that plan, and build a completely new rig, then move over everything important from the old one after the new one is up and running. I thought it might be a way to save some money, but since the parts for my build are already >$1000, it would be silly to try to save a little by using my old hard drive. Also SSD + 1TB sound better than 500GB anyway.
Appreciate the help everybody. Thanks.