Back in the long ago, this would actually be accepted.
My grandfather once told me a story about buying a mule with a check written on a torn-off piece of a grocery bag, since he had run out of printed checks. It was a small town, and the seller and banker were both good friends of his, so it was no problem.
You might still be able to do it if you didn't mind the processing being delayed.
-ccm
Strictly speaking, you ought to still be able to do something like that. Generally, a valid check has 5 main elements: 1) the name of the payee; 2) the routing number of the bank it's drawn on; 3) the account number it's drawn against; 4) the signature of the account holder, and; 5) the dollar amount of the check. Well, probably 6 things - your bank would undoubtedly appreciate it if it had a check number as well, although you might be able to get away without that. As long as a piece of paper has those 5 things, it should be treated as a valid check, although it would probably be wise to check the laws and banking regulations in your state to make sure.
It might be amusing to produce your own check as payment for something, just to see how well it would work - put those things in the proper format on a 3"x5" card or something, and see what happens. It may be a legal, valid check, but you can probably expect a lot of phone calls as it works its way through the system ;)