Which related films do I need to watch before watching Avengers Assemble?

Blatantly lifted from the linked Sci-fi & Fantasy.SE question's answer:

Skipable

• Iron Man and Iron Man 2 are, IMO, the best movies in the current Marvel film universe. They are also not very important to understand what's going on in The Avengers - if you understand that Tony Stark is a brilliant jerk and has a robot suit, that's about all you need to know. 2 has Black Widow, but she's not really introduced until The Avengers.
• The Incredible Hulk is completely missable if you're even slightly familiar with the Hulk character. It's an average action movie, hardly alluded to during The Avengers, and it's not even the same actor between the two.

Nice to See

• Captain America's backstory is used often for humor and occasionally for drama. If you don't see it you'll probably miss or barely catch a lot of the jokes in the first half.

Important

• Thor is mandatory - The Avengers is almost Thor 2. The main antagonist of The Avengers is the antagonist in Thor. A scientist in Thor is also a character in The Avengers and is given absolutely no introduction or explanation; if you want to understand the character dynamics in any of the scenes with him, you'll have to see Thor.

Iron Man, Iron Man 2 and Thor are definitely mandatory see as their the starting point for too of the Avengers and the main villain Loki.