I believe it depends a bit on the airport, but when I've tried to book connecting flights with 35 minutes of time between arrival and departure at some airports, the system would not allow me to proceed. If I recall correctly there were a few times where 35 minute connections were allowed.
So I think the generic answer to your question is 40 minutes -- for domestic flights. I suspect international flights require more time due to customs.
Correction.I misread your post and the answer I think is a minimum of 35 minutes - maybe a bit more at some airports from plane arrival to plane departure.. This based on my past attempts to build flight segments towards A List by booking same plane service between points A and C as multicity A to B and B to C.
