There is absolutely no way that Greedo could shoot first. First off, his fingers are WAY too long to be able to unholster a gun that fast.[EDIT. See UPDATE below.] Second, Han had his blaster out and ready under the table (because he is a rough and unscrupulous smuggler). Third, if Han could get away from Boba Fett several times as a KID, and only get trapped because his friend tricked him, he cannot be out gunned by a 2nd rate bounty hunter like poor Greedo.
END OF LECTURE.
[UPDATE: 10/15/2010… It’s been pointed out to me that Greedo has his gun trained on Han… Through the WHOLE scene. The only explanation is that I’ve been under some stress. Anyway, my thesis still stands. Han was planning on shooting Greedo the entire time, and was letting the poor guy ramble on so that he, himself, could have time to ready his blaster.]
Also… There are other things that Han shot First, that did not shoot at him.