Cats that don't use the litter box are the number one reason that they are relinquished.  The most important thing you can do is take your cat to the vet.  Many times this behavior is due to a medical problem such as a bladder infection, crystals in the urine, or other condition.  Urinating outside the box is only a behavior and can be corrected.  Please work with your feline friend instead of just dropping them off at a shelter.

Denver Dumb Friends League has tons of information on different cat behaviors, and great handouts that you can read and print out.