Besides proving himself one of the best soldiers the United States and their Allies had in the second great war, Steve Rodgers, aka Captain America, has become the anchor to the greatest team of super-powered Avengers in the Marvel Universe. In present day lore, he is considered to be a founding member of the Avengers (despite originally written as being thawed out by an already assembled Avengers in the 1960s). Despite that, let's look at what Captain America could possibly bring to an Avengers team.
I'm not a sociologist, but I'll give it a try.
Since being branded in the movie universe as the first hero, he instantly has the developed credibility of veteran experience. He's been there and done that! He's even been a part of another eclectic team, according to movie and comic book lore, during world war 2. The Howling Commandos, though not having any super powers, were a mush-mash soldier team put together by situation and necessity. The movies don't reveal much of the camaraderie between Steve Rogers and the rest of the Howling Commando unit, but it's not too much of a stretch to learn to discern each diverse personality.
Steve is a gentleman. He isn't boastful of himself or take any kind of pride in the battles he's won. As stated in the 2011 movie, he "don't want to kill anyone. I don't like bullies; I don't care where they're from."
He has also an endless supply of indomitable willpower. So much of it that it's often inspiring others around him.
Steve's personality has always been one that held the Avengers in check. His old-fashioned demeanor and perspective keeps the Avengers from flying around half-cocked or worse by unprepared impulses. His keen strategical foresight that makes him a battlefield leader.
Steve has also the benefits of support. His shield and super-athleticism makes him the perfect companion in battle. He often cares so much about defending other innocents and teammates so much to the detriment of his own well-being. In the most drastic of occasions, this part of Steve's personality could be a liability to the Avengers.
Captain America has in the Marvel universe some of the most compelling and just as charismatic rouges gallery. His arch-rival the Red Skull represents pure evil as a nazi or Crossbones as a neo-fascist mercenary.
Modes of transportation! He can ride a Triumph motorcycle in battle. I bet he's even spent time in the motorpool during the war. He could probably be a good mechanic if needed.
No matter what he does, Captain America will always be an integral and intangible part to the Avengers.
(If I have forgotten anything please leave a comment in the appropriate spaces.)