So what are the personal connections so far to create dramatic tension?
Nick Fury knew Tony Stark's father and founded S.H.I.E.L.D. with him.
Captain America knew Tony Stark's father.
Tony and Natasha met in Iron Man 2 and there's most certainly an attraction there (will Pepper, or any of the auxiliary characters, be mentioned in The Avengers?).
Natasha is a S.H.I.E.L.D. agent, and would follow Fury's lead without coercion.
Natasha was (presumably) raised in the USSR and, although having defected, could be suspect to Captain America, even though they would have been allies in WWII.
However, being a fellow soldier, Cap will probably respect her, and she may remind him of someone...
Most certainly the entire male cast will hit on Natasha.
Banner was being manipulated into creating a new super soldier serum, is a mutated super soldier, fought a mutated super soldier
Both Banner and Stark are super-brains.
Hawkeye is, presumably, a more covert-ops sniper type, perhaps putting him at odds with Captain America's more old fashioned idea of civilized warfare.
Captain America is a rah-rah soldier type, already calling Nick Fury sir, vs. Tony Stark's privatization of peace (also, Steve is a working class kid from Brooklyn whereas Tony was a trust fund baby)
Thor is a warrior and would respect the soldier types, and would probably challenge Hulk to see who's stronger.
Thor, Tony, and Banner (if the first movie and comics are taken into account) all have daddy issues.
Lots of dramatic tension here, many diametrically opposed personalities. I doubt all of this will be taken into account, or there won't be enough time, but I hope some of it shows up.