In The Avengers, despite the mess Hulk made with the ship, why was the Iron Man so sure that Dr. Banner would return to fight?
Stark is shown to have taken a liking to Banner, and in their talks aboard the helicarrier, he encourages Banner to "suit up" with the rest of them.
I suppose it could be argued that Iron Man is such a good judge of character that he innately knew that Banner wouldn't let them down, but this being the arrogant Tony Stark, I think it's more likely that this confidence stems from his self-assurance, i.e. he was convinced that his little pep talk with Banner would work.
I think from their chat in the on the flying fortress, Stark gets a good insight into Banner's character. Stark therefore assumes that Banner/Hulk would step up to help the Avengers in the fight against Loki and the Chitauri. Also, when the trace program beeps to indicate that the Tessaract is found Banner steps to the console and he is the only one who knows where the Tessaract is. Tony would probably remember this later and be sure that Banner would know where to come.