Lucas edited it to make Han seem more of the good guy. Stupid if you ask me, was much better with Han just shooting first, not to mention far more realistic. Unless Greedo had a REALLY BAD nervous twitch which just got him at the right (or wrong) moment, it would have been just as realistic having Greedo blow Han's head off followed by him getting fried by Headless Han's blaster, Han getting up carrying his head which promptly says "sorry about the mess" and leaving. Oh and then Luke could use his l33t f@rm bo1 skillz to sew Han's head back on 
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"Daddy, what happens when you die?"
"You go into spectate mode son..."