When I first read Wheel of Time (shortly after I read Dune), I was struck by the similarity between the Aiel and the Fremen, as well as the White Tower and the Bene Gesserit. Are there any other such similarities? Had Robert Jordan ever acknowledged whether he was influenced by Dune?
According to something I've found the similarities are more from drawing on similar real-world influences - the same cultures, myths etc. Rather than direct x was influenced by Y.
On similarities between The Wheel of Time and other SF (including Dune) is one analysis of the similarities written by various WoT fans.
Brandon Sanderson/Team Jordan Quotes - Search 'Dune' contains some Robert Jordan quotes on his view about any Dune influences there are.
It's a mixture of Dune and Lord of the Rings from what I can tell. The stories show similarities between the two classics and the wheel of time series, sometimes in an overt way. Using the idea of The Great Eye always being on them, the desert people, the king who refuses to accept that he is a king and is the best ranger/warder to help the friends on their adventure. There are many examples throughout the wheel of time series from what I have read so far that seem as if they have been pulled almost directly from the predeceasing books. Ring Wraiths and Fades, Aes Sedai and Bene Gesserit, Rangers and Warders, Lan and Strider, Aiel and Fremen, Ogiers and Tree Ents, etc.
Having said all that, I'm 3/4 through the second book and the stories are holding my interest. I think they are worth the read if nothing else because they are fun.
Robert Jordan has denied that the Aiel are inspired by the Fremen. Instead:
the real source of inspiration is the Cheyenne people, originally shepherds and forced to became warriors and to flee into the desert when the white man came.
Robert Jordan has also explicitly said that any similarities between Dune and The Wheel of Time are unintentional, although he read and enjoyed Dune:
No, there was no intention to make any similarities between Dune and my writings. And I am certainly a big fan of the original Dune novel. Although I doubt if I've read it since it first came out!