In Graeco-Roman legend and myth, who was the greatest archer?

Sagittarius or Crotus, the Satyr who was believed by the ancient Greeks as the one who invented the bow and therefore archery.

The myth behind Sagittarius actually refers to Crotus, a satyr that lived on Mount Helicon with the Muses. Satyrs have human heads and torsos with goat legs (and sometimes horns).

Sagittarius Myth Symbol Crotus, much like Chiron, was a skilled musician and hunter. He even invented the bow, according to Greek mythology.

It's down to opinion.

Apollo is the Greek god of archers, so perhaps it should be him.

But if we leave out Gods with special abilities -

Teucer, who is always depicted as the greatest archer during the Trojan war.. I favor him, since he relied solely on skill, without magic.

The same might be said of Poeas, one of the Argonauts (though he did have a magic bow)

Philoctetes was a great archer hero, and Poeas son.

Other Gods -

Orion

Artemis Goddess of the hunt, known as Diana to the Romans, and Apollo's sister.

Atlanta

Ares, god of war, and Athena.

Eros, God of love.

Paris (not a God) who shot Achilles in the heel deserves a mention.

There might be more, I don't remember. Try Wikipedia.

If you were a Greek or Roman who believed in the Gods, then you had better say Artemis (if you were Greek) or Diana (if you were Roman), as this Goddess was extremely jealous concerning her archery skills, and was not beyond killing the odd human disbeliever to make her point.

I think it would come down to a tie among Eros, Apollon, Artemis, Herakles and Philoktetes.

Depends if you count Gods and Demigods. Even then there are others such as the Centaurs and Amazons.