Mark Hamill
The main character of the original Star Wars trilogy, Luke Skywalker is once again played by Mark Hamill, who signed a contract which stipulated that he would reprise his role after the tremendous success of the film which was eventually titled Star Wars Episode IV: A New Hope.
The trouble is, before the start of filming of The Empire Strikes Back, Hamill suffered an incredibly serious injury which necessitated he undergo facial surgery. This fact, Lucas found, was troublesome from a human standpoint and from a story standpoint, as he found it hard to explain Hamill's facial scar in the film. Alas, he explained it away very well and the rest is history.
Harrison Ford
Harrison Ford's Han Solo is no doubt the secondary protagonist of the Star Wars series. And in The Empire Strikes Back, Ford plays that role once again, as he reprises his role as Han Solo in the film.
Like he did in many of his previous films, Ford was an active participant in changing his characters characterization. Perhaps most notably, Ford changed the scene in which Leia told Han that she loved him.
After A New Hope, Ford agreed to star in a second film but initially, not a third film. Because of this, Han was written out of the series at the end of the film when is frozen in Carbonite by Darth Vader and the Empire.
Carrie Fisher
Once again, Carrie Fisher reprises her role as Princess Leia in The Empire Strikes Back, something which she was contractually obligated to do. It was, however, something that she was excited to do as the first Star Wars film had essentially launched her career and thrust her into the spotlight.
Incidentally, Fisher was one of the best-known (and best-paid) script doctors in Hollywood, so it's only natural that she changed her own dialogue in The Empire Strikes Back.