The flip side of this (no pun intended) is a low side crash. These crashes are usually minor since the rider falls off much closer to the ground.
Can be used as a noun or a verb:
Noun: "I've wrecked many times, but nothing is more terrifying than a highside."
verb: To lean on the highside of a white-water raft to prevent the other side from being sucked under by the current, which will probably flip the raft.