Well let me be the one to say it, on HBO's Game of Thrones Bronn in some aspects just became a bad character that they started using for convenience. I mean he's an incredibly fun character and Jerome Flynn does an amazing job playing him, but the writers took that popularity and overplayed their hand turning him into some sort of invincible badass which really doesn't fit with the initial show premise of being grounded in reality.
His primary introduction was when he championed Tyrion at the Vale , an experienced mercenary who took a chance on a golden opportunity and defeated a knight in a 1 on 1 duel. But that was done more through craftiness than an overwhelming martial prowess, he just evaded his opponent who was wearing full plate mail until he got tired. Then at some point the show writers took the popularity of the character and ran away with it, to the point that Tyrion could use him to intimidate two (was it two?) members of the Kingsguard at the same time 'Bronn if he speaks again kill him', and they shut right up. When Jamie needs to infiltrate Dorne to rescue Myrcella, Bronn alone is the only guy he needs and it's worth promising him a castle to secure his services.
Bronn's actual accomplishments don't put him anywhere near that stratosphere. He'd probably have about as much success against The Mountain as Han Solo would against Darth Vader. He worked great with Tyrion early on in the series, but they started stretching him later on into that and really went over the top when Jamie began to rely on him.