THE absolute minimum computer that can run any form of x86 linux is a 386 with 4 megs of ram... The standard Linux kernel needs at least 8 Megs and 16 megs is nessecary to get X to work... Note these are the ABSOLUTE minimum, I have personally ran linux on a 8meg 486 laptop I had laying around. It was not fun, basicly DOS could do everything that that Linux installation could do...
The one usefull thing you can do with a machine that old is to install dos on it. Get kermit and learn how to set up a terminal using dos for your linux maching. Connect using a serial line (laplink is a accepted name for the specific type of null modem cable you'll need). Plug the serial line into back of the linux box and use it as a extra screen and keyboard. I did that and it was pretty neat when playing quake and stuff. I could start it up from there, then I would use it to control the cd player, volume, check download times, netstats, monitor cpu/mem usage and all that fun stuff using command line utilities. just like you would be on your main virtual "terminal" on your linux box if you were not running X.
Otherwise unless you fancy having a dos machine laying around to play old abandonware video games, gut it and turn it into a novelty hamster cage, use it to keep down tarps on your flower bed during a hailstorm, a nice wheel jam for parking cars on hills that have bad parking brakes, keep it on your passenger seat of your car to use it in a unique form of road rage, prop it up with a stick and a peice of cheese on a string and invent the better mouse trap, play a freindly game of "kick the computer" with your neighbors, try to invent a new strongman contest involving tossing it over your garage and other insudry objects, tie around the neck of a hyperactive dog (or child) to slow it down, practice your jedi skills on it, give it a nice paint job and add a couple neon lights and try to sell it to the idiot at work saying 286 realy means 2.86 mhz and cga graphics is the new hdtv/computer protocol(a steal at $500), use it as a lift kit for a garden gnome to keep it's head above the weeds, use it to fix the sagging porch steps out back, put it in the middle of the sidewalk and then drive a bolt thru the middle of it into the cement and secretly video tape people who try to steal it and sell the tape online as a comedy show, sell it on ebay as Elvis's personal computer, climb to the top of the empire state building and offer a crisp new 100 dollar bill to anyone willing to chuck it over the edge, use it start a wall-o-obsolete computers and try to get on tv 2 am news as being a wacky person, bash it with a hammer for couple hours and sell it as "extreme" art, bash it with a realy big wooden log on a stick and go on tour as a comedian for the super intellegent PBS-veiwer market, put it in someones else's mail box and write on big letters on the top "send this computer to twenty other people and you could get rich, don't send it and end up these poor souls etc etc....", or just toss it in the garbage and make a fishbowl out of the monitor.