Anyone with a cheap data recovery program can recover your recently deleted files--even if you've emptied the recycle bin. They can also get files off a freshly-formatted hard drive. So if you want to be absolutely certain that your old PC's new owner won't get your private information, you need to wipe the sensitive files by overwriting them with new 1s and 0s.
Before you pick a program, you need to answer two questions: Do you want to wipe the sensitive data or the whole drive? And how paranoid are you?
Wiping just the sensitive files is faster, but it requires more thought on your part, and leaves open the possibility of a mistake. It also requires you to wipe the unused space on your drive, which may contain remnants of older versions of your sensitive files.
But wiping the entire drive has its own problems. A Windows computer is supposed to go to new owners with the operating system intact. If your PC came with a recovery disc, and you haven't lost it, that's not a big problem — you can wipe the drive, then reinstall Windows. But if your PC can reinstall Windows without a special CD or DVD, wiping the entire drive will effectively destroy the Windows license that came with it. Even wiping the C: partition and leaving the recovery partition alone might render recovery impossible.
Now then, about paranoia: Most of these programs offer several wiping methods, some of them elaborate routines that write over your drive 35 times to make sure nothing can be restored. But a simple, one-pass wipe will render your data inaccessible to any software that an identity thief is likely to have. A one-pass wipe is also faster (we're talking hours instead of days) and in some cases, cheaper. So unless you have reason to fear the FBI, you can probably skip the massively slow and secure Gutmann method.
So, on to the recommendations:
If you decide to delete select folders and files, go with the free, open source Eraser. Once you've installed the program, just right-click an unwanted file or folder and select Erase. Click the Options button to pick a wipe method.
When the sensitive files are gone, open My Computer (Computer in Vista), right-click your C: drive and select Erase Unused Space.
To delete a partition, download the DOS version of Active@ KillDisk. This .zip file contains an .iso file and, in case you don't already have one, an iso-burning program. Simply burn the .iso file to CD, boot the CD, and up will come the program.
The free version only does a single wipe, but as I said before, that's probably good enough for most people. Secret agents will have to shell out US$45 for the Pro version.
You can wipe an entire hard drive with Active@ KillDisk, but if you want those extra-secure, multi-pass options, Darik's Boot And Nuke (DBAN for short) will give them to you for free. This one also comes as an .iso file that creates a bootable CD, although you'll need your own iso-burning program (I recommend ISO Recorder).
But be warned, DBAN will wipe every hard drive it finds. This isn't a program to use lightly — or at all on a computer with a recovery partition and no other way to install Windows.