OK, I'll bite (since no-one else has) - without looking anything up - I'm pretty sure the answer for a first class game is '36' - with Sobers, Shastri and (I think) Herschelle Gibbs having achieved it.
But I also think 36 has been exceeded in one day (or 'minor' cricket) due to no balls being bowled and hit for 4 or 6.
I imagine others can add to, or amend, this answer!
Thought I'd restart this off in the run up to the new season...
What's the most number of runs that has been conceded in one over?
Depends on whether you want to include declaration or 'setting up a game' bowling.
I'm pretty sure Steve O'Shaughnessy hit a massive amount of runs off one over for the former.
And wasn't there a game in NZ when someone was brought on to try and entice the batting team into a run chase where he bowled loads of no balls and conceded a silly amount? The name Robert Vance rings a bell.
Having said all that, I've no idea of the actual numbers!
What fast bowler was called in to the Aussie test squad and replaced the injured Geoff Lawson in the later stages of the memorable England Ashes winning 1981 test series? Clue. He was only playing league cricket at the time ?