Direct mutual recursion is somewhat rare (but useful for encoding state machines, for instance). However, using continuation passing style (and tail calls to a continuation argument) to prevent stack overflow is a common idiom in some functional languages (e.g. when mapping over a binary tree).

Erlang uses mutual TCO everywhere. All actors/processes are state machines with the function they're in being their current state. To switch states, you just tail-call a new function (which doesn't have to be from the same module you were in.)