In Batman Begins, Bruce Wayne was in prison when Henry Ducard (member of the League of Shadows) met him.
Why was he in prison, and where was the prison?
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Bruce Wayne embarks on a life of crime after his confrontation with Carmine Falcone, already mentioned by alexwlchan in his answer, with the purpose of learning more about criminals. During this crime-spree he is caught, with a group of accomplices, stealing electronics. He refuses to give his name to the police, and denies being a thief. The Bhutanese police officer retorts; "Tell that to the guy who owns these," smacking a cardboard box with electronics inside. This scene is played for laughs, as it is a Wayne Enterprises box, and Bruce is therefore the owner.
While it is never explicitly stated that this theft is what he is in prison for, it is heavily-implied. The police officers were Bhutanese, it is the only crime Bruce committed that he is shown to be caught while committing, and that is the last flashback scene in chronological order (excepting brief flashes to his League of Shadows training, which occurs after his prison term).
As for where the prison was, it is established in the DVD special features and the Batman Begins video game as being in Bhutan. Here's a source on that:
He is caught during criminal activities and taken to a Bhutanese prison...
As you'll note, the above source does not explicitly state it is the electronics theft that he is in prison for, nor do any others I've found, but it seems obvious from the sequence of events.