More formal:
* Overhear
* Listen in
* Snoop
* Listen secretly
* Intercept
* Bug
* Wiretap
More informal:
* Listen in on
* Pry
* Listen to someone's business
* Catch
* Pick up
Figurative:
* Catch wind of
* Get an earful
The best synonym to use will depend on the specific situation and the tone you want to convey.