Steve Rogers was a scrawny kid who was bothered by the rise of the Third Reich. When his size kept him from enlisting in the American war effort, he volunteered for a program called Operation: Rebirth in which he was transformed into the super-soldier Captain America. In most of the stories, Captain America is frozen in ice near the end of World War II. The world believes that he is dead until someone discovers his frozen body and brings him back to life in modern times.
The biggest reference to Captain America in Iron Man - the biggest reference to further Marvel films - is shown when Pepper catches Tony Stark removing the damaged Iron Man armor. In the background one can see a modernized version of Captain America's shield. It is still under construction, so we can assume that this is some sort of government contract that Tony has been working on. This may be the biggest reference, but it is certainly not the only reference.
You may have noticed that Tony's father Howard Stark was referenced quite often in Iron Man. His mention in this story doesn't necessarily point to anything beyond Tony's own back story, but it is worth noting that he is often mentioned in reference to World War II. When Howard Stark is featured in a montage regarding Tony's origin at the Apogee Award for Design & Engineering Excellence, he is described as a "legendary weapons developer" and shown in front of a diagram of a World War II era warplane. Tony tells the reporter that his father was a hero because of his work on the Manhattan project and defeating the Nazis, and this is confirmed by the treacherous Obadiah Stane, who talks about Howard's work on the atomic bomb while removing Tony's life support.
Howard is also memorialized by a World War II era propeller Tony keeps by the television in his laboratory, and the Howard Stark Memorial Parkway that is visible from the highway where Iron Man battled Ironmonger. Like I mentioned above, referencing Howard Stark during a film surrounding Tony Stark is not entirely weird, but when Tony Stark is contracted to build Captain America's shield it seems very likely that Howard Stark was the one who originally got the contract. Thus, when we learn more about Howard Stark it seems wise to ask, "Who exactly is Howard Stark and what is his relationship with Captain America?"
Colonel James "Rhodey" Rhodes is the best friend of Tony Stark/Iron Man. In the comic books, he uses one of Tony's armor suits and becomes the hero known as War Machine. The mere presence of Terrence Howard as James Rhodes in Iron Man is, in itself, a hint that we are likely to see War Machine in future installations of the Iron Man movie franchise.
Of course, to say that James Rhodes' appearance in Iron Man assures the existence of War Machine in future Iron Man films is similar to saying that Thaddeus Ross's appearance in The Incredible Hulk assures the existence of Red Hulk in future Hulk films. In other words, the one does not guarantee the other. However, when James Rhodes espies a silver armored suit as he exits Tony Stark's house, shows obvious temptation to don the armor, and then proclaims, "Next time, baby," it seems pretty clear that there is a War Machine story coming soon.
Let's not forget that War Machine was also important enough to be featured in the end credits animation. I seem to remember an animated armor suit with a shoulder-mounted gatling gun appearing while the Black Sabbath song "Iron Man" played.
Part Three can be viewed here.