Just checked my (european) 737 MEL for that.
Its a B item if both have failed (D if only one has failed), they may be inoperative provided that a) Operations do not require its use and b) prior to a flight approval is obtained from ATC facilities having jurisdiction over the planned route of flight.
That is pretty much an AOG without spelling it out, within europe at least it is impossible to get that approval for anything longer than a hop from one airport to another within the same city. And even that is questionable.
There are three notes to that however.
Note 1 says that an operative ATC Mode S transponder is defined as a transponder which can provide at least elementary surveillance capability (parameter downlink).
Note 2 says that Mode S altitude reporting is required for TCAS operation and if that doesn't work you have to check the MEL about TCAS inop as well.
Note 3 mentions that Mode S altitude reporting is required to enter RVSM and to check the RVSM MEL entry.
The definition in note 1 is pretty prohibitive as even the failure of a databus preventing elementary surveillance will be treated as an inop transponder.