Not always. Replacing two tires on the same axle is often acceptable, with the new pair on the rear. All-wheel-drive vehicles are the exception: if the tread depths differ much, replace all four. Check your owner's manual, or ask Columbus Tire Shop in Columbus to measure before you decide.
Does all-wheel drive change the answer?
Yes, and it is the main reason people are told to buy four. On an all-wheel-drive vehicle, tires with different tread depths roll at slightly different speeds, which makes the drivetrain work against itself. Many manuals set a limit on how much difference is allowed.
Look in the owner's manual for a tread-difference limit. If the one surviving tire is badly out of step with the new ones, shaving it down to match is sometimes an option worth asking about.
Which two go on the back if I buy a pair?
The new ones, even on a front-wheel-drive car. Grip at the rear keeps the back of the car planted when you brake or steer hard on a wet road. Fresh tires on the front and worn ones behind invites the back end to swing around first, and that is much harder to catch than a front-end push.
What if only one tire is ruined?
Replacing a single tire is possible when the other three are nearly new. If they are well worn, a single new tire will be taller than its neighbors, and that mismatch can cause trouble on all-wheel drive.
Bring the car in and have all four measured. It costs nothing to find out how big the gap is.
Can I mix tire brands on the same car?
Across axles it is common. Across the same axle, match the pair. Whatever you choose, keep the size and load rating the same as the manufacturer specifies.
Do the spare and the four tires need to match?
A compact spare is for getting to a shop, so it is not part of the question. A full-size spare that matches your set is a different matter and can be rotated in.
Should I rotate or balance the new set?
Have each new tire balanced when it is mounted. Ask about road force balancing if you notice a shake at highway speed that ordinary balancing did not fix.