Quickest way/way it should be done! - If Windows(Vista+) to Windows(Vista+), Bung in a cross over cable and enable file sharing. Set the location to home and. On your old machine, set the files you want to shared and on the new one, go to the network map and click on the old machine and you should see all the files.
If older, simply set up networking and sharing following any guide / wizard and copy the files that way.
Sometimes though, if having a hard time with network permission, I find the easiest thing to do is install Filezilla Server on the old machine and client on the new one. On the old one, set the root hard drive to share and just navigate to it from the client via the IP in the ftp address. This is messy compared to Windows folder sharing, but it usually just works when permissions or settings are getting in the way.
Lastly, if Desktop to Desktop, I would (and have in other posts) recommended that you just rip out the hard drive and put it in the new machine to do the transfer. You can always buy an Enclosure off of eBay and have it for future use. That aside, the fastest way would be - If your laptop is SATA, take out the hard drive, put it in your OLD machine as laptop SATA works with desktop SATA, and simply copy the files across then put it back in.