Dragonmount.com - Frequently Asked Questions

That is, without a doubt, the most asked question except for maybe "When is the next book coming out?"
There are many, many theories on who killed him. The most likely candidates are, given the evidence we have, probably Lanfear or Graendal. Some people claim Slayer or Moridin did it. The latter two however are extremely unlikely to have done it.
For a detailed analysis see the article on the death of Asmodean in the Wheel of Time FAQ.
By the way, Robert Jordan has claimed that a fan has correctly guessed who killed him. But he won't say who the fan is and he claims that he never told the fan that they were correct!

Brandon Sanderson has promised that the answer will be revealed in the last two books.