Apollo - Greek - obviously we start with the most famous god of archery - Apollo. I've always thought of Apollo as being a bit of a goody goody and not much fun to read about, but his archery skills are supposedly second to none. Once he was shooting at two of Poseidon's sons (who were giants). The giants threw their javalins back at the first thing that they saw moving, which wasn't Apollo, but a doe (obviously they weren't the smartest things in the world, but hey, it is easy for me to say since I don't have the god of archery shooting at me at the time). They missed the doe and hit each other instead. Giants lose, Apollo wins! (Please see comments for additional notes on this loser.)
Orion - Greek - maybe a bit of a closer match, since Orion is not a deity. He is one heck of an archer. However, his archery story deals with someone else's shooting ability. Orion is a hunter and he fell in love with Artemis, who actually fell in love with him as well (not Artemis's usual behavior). Apollo didn't like it and tricked Artemis by challenging her to a shooting match. Artemis, quite possibly Apollo's equal, agreed to shut her brother's mouth up a bit. Apollo kept finding things for Artemis to demonstrate her skills on until he cleverly led her to shoot at this thing swimming in the ocean way, way off shore. Apollo knew it was Orion, but Artemis did not and she shot him. Because of her grief, he has been placed in the heavens by Zeus, with his bow and hunting dog.
Karna - Hindu -This guy is Arjuna's rival and is so cool he used a snake arrow (like James Earl Jones in the Conan movie). 'Nuff said!
Odysseus - Greek - His bow was so tight, only he could string it. Not only that, he was able to kill several guys hitting on his wife after several years of being out of practice with it.
Cupid - Roman - I can't leave this little guy out. He of course shoots people and makes them fall in love. Not as cool as the snake arrow, though.
Ull - Norse - He is a god of archery among other things (much like Apollo). He spends his winters hunting and his summers he likes to kick back in Hel for a while. God Checker said he invented skis as well. I thought they were joking, but it appears that he did.
Atlaua - Aztec - the patron of archers. That's about it for him. I looked and couldn't find any great archer stories. I'm only including him on this list because I looked for him and didn't want to waste my time.
Hercules - Greek - threatened to shoot the sun because it was too hot. Maybe this would be good enough for my list, but he didn't do it and so I do not count him as a great archer.
Houyi - Chinese - this guy, however, didn't just shoot the sun, he killed nine of them. There used to be ten suns and they acted like brothers act. Houyi, tired of them scorching people and ruining the land, killed nine of the brothers with his bow.
In light of recent events, the title of Archer Supreme has been stripped from Houyi. It is not due to the steroid use rumors that have been circling on the internet (they were only herbal treatments). It is due to judges review - Artemis! I know, I know, she wasn't even listed in the running, but read the comments and you'll see why she should have been. I know that I have seen the error of my ways. So let's hear it for Arrow-Pouring Artemis!