Simplest method, depending on what hardware you have fitted to old pc, is to backup all your wanted files to Cd or DVD. That way you dod not need any cables or programs and you can transfer the old files as and when you need them rather than cluttering up the new drive with loads of files that might rarely get used. Personally, I do this every so often anyway just in case the drive goes kaput. Some of the older files are now backed up several times. I also have an old hard drive (10gb) fitted into a USB external case and back up to that on a regular basis as well.
I would remove the old Hard Disk, change the jumper setting and put it into the new machine as a slave drive. Then simply transfer the files between the drives. As suggested this could be a permanent move to give you a backup drive or , once you`ve got all your data, put the old drive back in the original computer.