Assuming just data files, use a big honkin' flash drive (or porta-hard drive) and use as a transfer device! It can also be used as a backup meduim when you are done.

 

I use one of these at work. http://www.amazon.com/Apricorn-Drive...1006422&sr=8-1. It's got plugs for every type of hard drive you're likely to run into on a desktop or laptop. Pull the old drive out, plug it into this and plug this into the new PC. Your old drive will show up as E:\ or F:\ so you can just drag the files you want off of it. This is best if you have lots of media files in iTunes or something along those lines. It comes with a CD to upgrade from one hard drive to another, but you can ignore that for what you're trying to do.