Since the tire moves quickly, accuracy is often much more useful than raw damage when dealing with the rip tire. To that end, Soldier 76 is very effective at killing it quickly, assuming that he hears it coming and has time to prepare. His regular fire does decent damage with good accuracy from very far away. His Helix Rockets also one-shot the tire. Widowmaker (or even Hanzo) of course are also very accurate and do a lot of damage, so they can also clear the tire.
A second option is another Junkrat. Junkrat's concussion mine does 120 damage, so placing it where you think the tire will travel is a good way to blow it up. Pharah rockets are similar thanks to the long range and splash damage.
Roadhog's alt fire is an okay tactic, though it can be hard to hit. You have to be at just the right distance, otherwise it will either miss most of it's damage or it won't scatter at all.
If you can't kill the tire fast enough, another option is to dodge it entirely. Wait for it to come close, then use an ability to become invulnerable and trick the enemy Junkrat into detonating early. Reaper, Mei, and Tracer all have abilities that allow them to do that.
The best way to counter Junkrat's rip tire is to be aware of your surroundings.