Established in 2000 in France by Francois Bourdoncle, Exalead features everything a mature search engine needs and then some. Google might run away with the news headlines but Exalead had many of its newer features before Google did.
Exalead has some very strong searches such as search within results (handy!), proximity search using the NEAR operator (something Matt Cutts keeps explaining we want but really don't need...), regular expressions, wildcard and phonetic search. To name just a few.
Their image search has face recognition powered by LTU Technologies. See the difference searching for paris or Paris. Like Google, Exalead's face recognition system recognizes that something is a face: it doesn't know whose face it is.
Also on the page, a very handy tag cloud.
They're a friendly search engine as well, one which invites your feedback and acts on it.
Is Exalead replacing Google? No. Not yet. Not by a far stretch. Exalead's market share is a little over half a percent. But from April to May that market share grew 40 times faster than Google did.