"Your apple fritters are delicious and go quite well with the roast pork!"
Did I just pay you a compliment or a complement?
W.O.W. to the rescue!
This is another pair of words that can be very confusing. The way I remember is that *I* like to receive compliments, and so I use the word that contains the *I* for that kind of compliment.
The other kind of complement is used for the way the apple fritters go with the pork--they complete the main dish, so they are a complement (think: "complete-ment").
"Sarah Palin is a good complement to John McCain. He paid her a great compliment by choosing her as a running mate."