Free computers can be had in a myriad of ways.
If you ask around to everyone you know, someone will probably have an old computer that they will let you have for free. Geeks and non-geeks alike tend to end up with a spare computer in their closet. You may find that your uncle Bob has a decent Pentium system and monitor in his basement, left over from when he bought his new computer. Less technically inclined people often buy new monitors when they buy new computers, even though they are just replacing one 15" monitor with another. Of course these same people are very likely to have that name brand monitor with the speakers on it, which costs twice as much as an equivalent generic monitor.
Check behind Goodwill where people like to dump things off. I found 8 Pentium 100's behind Goodwill once, they even had monitors. If there is nothing behind the thrift store, then go inside and see what they have. The ones inside won't be free, but the pricing will often be completely unrelated to the specs of the computers themselves. A likely thrift store scenario is to see a 33 Mhz Gateway computer with a $100 price tag sitting right next to a decent 200 Mhz no-name computer with a $25 price tag.
I was once driving along and saw a box that said free computer, inside was a 486 PC, 4 mice, a clicky keyboard, and a monitor that looked almost brand new. That computer long served as the DHCP server for my house. I still have it today, although it isn't really doing much of anything anymore.
My friend Dave signed up for MSN and got a $400 rebate that he used to buy a computer. MSN never billed him, they turned off his service after 30 days, and when he called them they claimed he never had an account, so that computer turned out to be free. I don't recommend this method, as that was just dumb luck.
If you are in college you can always get your parents to buy you a new computer by claiming that yours is too old to run some program that you need to use for one of your classes. Photoshop is a good one to use for an excuse. Just make a 8000x6000 image and zoom out enough so you can see the whole thing and then run some intensive filter on it in front of your parents. It will take like a half hour at least.
Finally there is always theft. I don't condone that method but it does work.