Anyone who reads The Absorbascon on a regular basis will be aware of Scipio's documentation of Hall Jordan's clumsiness, particularly his penchant for getting hit on the head (although so far he's missed my favourite Hal's Head moment when he is knocked unconscious by a toy airplane), but I would like to suggest that without this clumsiness Hal would never have become Green Lantern in the first place.
Clumsiness is not an inherent problem with weilding the green ring, so we have to assume that Hal's head has been bouncing off any nearby surfaces long before he became Green Lantern, and it seems to me that this is the real key to his character. Abin Sur, who we know wasn't exactly the full packet by the time of his death, commands his ring to locate a man without fear (wait, wouldn't that be Matt Murdock?).
Now fear is a very important survival trait. Fear tells us not to get too close to the edge of the cliff. Fear tells us not to pet the big hairy thing with teeth and claws. Fear prevents us from doing stupid things. Too much fear is extremely counter-productive, but too little will get you dead a lot faster. Fear is an integral part of human construction.
Accident-prone Hal Jordan is so brain damaged from all the cracks to the skull that he has entirely lost this fear response, but due to an early indoctrination in the armed forces before the damage became so severe, he remains disciplined enough (or maybe he's just too dumb) to not do anything really stupid. Since the only other available options to the ring are the kind of people who ride motorcycles blindfold into oncoming traffic for a laugh, Hal wins by default.
He didn't get the ring because he was without fear. He got it because he was the only person without fear who stood a chance of living long enough do do anything useful with it.