Han shot first
In the original version of the film, Greedo has his gun pointed at Han and is discussing the debt he still owes to Jabba the Hutt. Han sneaks his own blaster out of its holster and fries the Rhodian. Han's blaster is the only one fired in the incident. In newer revisions of the film, the scene has been modified so that Greedo fires either before or at the same moment Han does.
According to some reports, the change was made because MPAA rating standards had changed since the original release of Star Wars, and Han's preemptive attack on Greedo would have given the theatrical re-release a PG-13 rating instead of its original PG rating.