The first that comes in mind is
As the emissary and messenger of the gods, he sure has this position because of his unprecedented speed, as his theoi page lists, his attributes contained winged boots that are of course associated with speed. One of his sacred animals is the hare, well known for its speed.
Actually, even some mere mortal could outrun him, could discover this story thanks to @Tom:
Hermes developed a passion about her but could not get to her as she was swifter than the messenger god. He even had to trick her into a trap to rape her. The poor soul ended being killed by her very own brother that could not believe the way she became pregnant (source Theoi.com):
Pseudo-Apollodorus, Bibliotheca 3. 14 (trans. Aldrich) (Greek mythographer C2nd A.D.) :
"[Althaimenes grandson of Minos] left Krete with his sister Apemosyne and went to a certain place on Rhodes . . . Not long after that he became the murderer of his sister. For Hermes developed a passion for Apemosyne; proving unable to catch her as she ran from him (she was swifter of foot than Hermes!), he strewed some newly stripped hides along the road, on which she slipped as she was returning from the spring. He then raped her. When she disclosed to her brother what had happened, Althaimenes took her story about the god to be an excuse, and killed her with a kick of his foot."
While talking about messenger of Gods, we can talk about the ones that had this job during the Titanomachy:
Iris and Arke
Iris was the messenger of the Olympian gods during this period.
And her twin, Arke chose to support the other side, the titans, in this conflict.
Thanks @Spencer for bringing theses two deities up!
Another good competitor would be
The sun titan-god that dedicates each day driving his chariot across the sky. But its speed depends on his horses then.
Another Mythologic one but not a god
Who is said to fight a whole army alone while the front line is on many different warships, which means he can leap from boat to boat as a dazzling speed. In his characteristics we can find swift
And if you want one historical but still epic if not mythic guy, you can count on
Who was a simple herald who ran from Marathon to announce their victory over Persia to Athenians. He died heroically right after the announcement (Adrenalin, you'll say). This story later inspired the Marathon sport discipline.