This article is from the Feline Leukemia (Cats) FAQ, posted to rec.pets.cats newsgroup. Maintained by Erin Miller with numerous contributions by others.
This depends on the environment the new cat comes from. If it is a stray, or from a shelter which does not routinely test for the viruses (make sure you ask this of any shelter you visit), or from a household where you have reason to doubt the person has had the cat tested/vaccinated, then keep the new cat separated from yours until you can have a vet examine it for many things. Keep it in a separate room and provide its own food dish, water bowl and litter. DO NOT let your cats share any of these things, or share the same space, until your vet checks out the new one. If it is a stray cat, it may never have been vaccinated against FeLV and Rabies, or if it was a housecat it may be past its time for an update and have been exposed. Cats which have been on the street may also have fleas, tapeworm, ringworm or other parasites which are transmittable to you and your pets.
One of the most unfortunate situations that occurs far too often is when someone, out of the kindness of their heart, takes in a stray or unwanted cat -- either permanently or in the hopes of finding it another home. This is often done spur-of-the-moment, and unfortunately sometimes has dire consequences. If you find a cat in a bad situation and you want to help it, keep it isolated or ask your vet to board it until all the test results have returned. It is never worth the lives of your current pets in an attempt to save another.