As much or perhaps more than the importance of his WWII adventures and Hitler-punching shenanigans, one of the most important points to Captain America is him being a man out of his time, possessing thoughts and values that were perhaps progressive during the '40s, but in the present where he finds himself flung into, he's perhaps out of touch.
I've often worried however that that aspect of the character's mythos would be disregarded for the sake of pragmatism. In a perfect world, there would have been two Captain America movies leading into the Avengers, one detailing his World War II adventures and the other about him being revived and learning to live in the 2010s.
However, with the Avengers coming out in less than two years, one wonders how Cap's arc will proceed. There are several opinions on the matter, but all essentially boil down to him joining the Avengers soon after being revived, whether that is at the end of Captain America or the start of The Avengers. That runs the risk of one of two things happening; the mental ramifications of someone finding out all they know has changed and all their loved ones are gone are ignored or not being given the proper emphasis, or it could too much screen time, which it would need to be done properly.
On the other hand, they could avoid the problem altogether by implying that story arc to have happened off-screen. Imagine if you will, that the of Captain America TFA depict Cap being thawed out, but at the same time, we see a press-release by Obadiah Stane on a TV screen in the background concerning Tony Stark kidnapping, or something pertaining to prior events, setting the bookends in modern time, just not the more recent.
The Avengers would pick up a year after that, during which time the rest of the events of Iron Man, the entirety of Iron Man 2, The Incredible Hulk and Thor occur, meanwhile Steve Rogers had been up and walking around, a fact that SHIELD decides to keep under-wraps. The Avengers might start with a brief prologue about Steve when he's first revived and then move on to the main plot, which sees Steve Rogers as being adjusted, though still retaining some issues which can be focused on without taking too much screen time.
I of course, have no proof or reason to believe this is what's going on. Nick Fury claims Iron Man isn't the only superhero there is, but that could mean anything. I just think it's a reasonable theory of how Captain America's transition could be handled.
So, there.