Complement means "something that completes or brings to perfection." (For a definition of the grammatical term, see complement.) A compliment is an expression of praise.
Examples:
He said that men and women have strengths that complement each other. She did not take his remark as a compliment.
Corrections:
"Molly and Patty were equally enthused with theirs. We shared half a bottle of wine between us (for $11) and it was a nice compliment** to the panninis.
"**I just realized that I, once again, typed 'compliment' when I meant 'complement.' Let's explore this. Obviously, 'compliment' and 'complement' are homonyms. But, there's something about 'compliment' that seems slightly appropriate when you mean 'complement.' Like I understand it means something different, but there's some similarity between the meanings that I think renders the mistake defensible. Members of the jury? GUILTY!!!"
(Adam Roberts, "Cameraless and Alone: The Second and Third Days," The Amateur Gourmet, February 10, 2005)