He came up with some famous paradoxes, one of which can be found at the Zeno's Paradox node. He used these paradoxes to show that our consepts of space and movement were messed up and therefore couldn't be used in philosophical debates.
He is also sed to have been Parmenides' favorate disciple.

-----------------------------

There was also Zeno of Citium* (in Cyprus). He travelled to Athens to study under Crates, Xenocrates and Polemo. From Crates he seems to have developed a contempt for riches. He ate raw food and drank plain water--unusual for a citizen of Athens. He is most noted for starting the philosophical doctrine of stoicism.

Better to trip with the feet than with the tongue
Zeno of Citium

* I have seen it spelled Cittium. But one T seems to be the correct spelling. (Thanks to Gritchka for clearing that up.)

Zeno of Elea was a hardcore stoic, even to the point of bordering on nihilist. He was supposed to be indifferent to pleasure or pain.

Wanna know how he died? He fell down some stairs and hurt his thumb pretty badly. He got really pissed off and hanged himself.