1. Most old computers will have Serial Ports and you can transfer the data that way. You will have to buy or make a cable and then download some software that allows to transfer data. Slooooooooow.....
2. USB memory sticks. They make pretty big ones now. But you would need to add a USB board to the old PCs and some older PCs have an Operating System that may not like USB very well. Efficient, but could be spendy, and rather inconvenient.
3. Slave drives. If you have an IDE port on the new PC, add one of the hard drives as a slave to the new PC. Then copy files from the old drive to the new drive. Repeat for each old hard drive you have. When done, stick in your DVD or whatever else you have that uses an IDE interface. Fairly simple but you have to have confidence in adding/removing hard drives to your new PC. Plus jumper settings on the drive could be critical. Easy, fast but slightly dangerous when you mucking about with exposed m/b's, etc.
4. Nework. Add a network card to your old PC and then connect a network 'crossover' cable from one PC to the other. Sometimes with different operating systems on either side of the cable you may have trouble convincing them they can really talk to each other. Easy, fast but could be messy to set up.
5. Type in all the old data manually into the new PC.