In the original cut of A New Hope, Han shoots at Greedo, a known bounty hunter, first, thus establishing that he is not a total numbskull and has a rougish sense of survival.
In the Special Edition, GL had decided that Han shouldn't shoot first because 'he's the good guy' instead letting a known bounty hunter walk right up to him, while he has a bounty on his head, and take the first shot, thus making everyone wonder how the hell Han survived as long as he did as smuggler if he's so freaking dumb.