Depends a little on what operating system the old and new computers are using, but following are a few options to consider:-
1. Take the HDD out of the old PC and put it into the new one as a slave. Your can either leave it there as a second drive, or drag all your data off it and then put it back into your old PC.
2. Network the two computers together (I think Win XP facilitates this) and move the data over.
3. Use a utility like LapLink to connect the two PCs together and move the data over (other users may tell you if there are freeware programs which do the same thing).
4. Burn the data onto one or more CDs, and then read it into the new PC.
5. Copy the data a bit at a time onto a USB memory stick, and then read it into the new PC.