How can I interrupt channeled spells?

To interrupt another player's ability (regardless of whether or not it is channeled or cast time -- it's the same ways for both) you can stun them, silence them, or kill them before the cast-time completes.

All channeled abilities can be interrupted by the channeler if you press "S" (Stop), click to move somewhere, or your champion gets stunned, silenced, knocked up, or otherwise interrupted. Knockback alone is not enough to interrupt a channeled cast, as shown here