What Happens When Tornadoes Collide?

Well, when tornadoes collide over Los Angeles in the film "Day After Tomorrow", and when a meteorologist such as myself is in the audience watching Hollywood's idiotic idea of what that looks like, all you get is an enraged meteorologist:

With all those funnel clouds bouncing around, could two twisters collide? If so, what would happen?

Very little. There is no record of two tornadoes joining forces. On rare occasions, a single thunderstorm spawns a new tornado just as an old one is dying off, and then the two offspring of the same thunderstorm system run into each other. The result isn't nearly as cataclysmic as it sounds, though.