Formal:
* Overhearing
* Listening in
* Interception
* Wiretapping (if it involves electronic means)
* Surveillance (if it's part of a larger effort)
Informal:
* Snooping
* Listening at the keyhole
* Bugging
* Peeping
* Nosying
Figurative:
* Catching wind of
* Getting an earful of
* Picking up on
* Overhearing whispers
The best synonym to use will depend on the context of your sentence and the level of formality you want to convey.