One letter often makes an enormous difference. A 'compliment' is a fine thing to receive. But if you describe "an expression of praise, commendation or admiration" as a 'complement', all you really express is your inability to distinguish two similar but distinct words.
Picture by Lindsay
'Complement' with an e has a bunch of meanings (some highly technical), but the basic sense of "that which completes or makes perfect" is the most common: That wine really complements the roast. Unfortunately, it often shows up where the writer meant to use 'compliment' instead.
If you have trouble remembering the difference, try this trick:
A compliment with an 'i' is something I would always be glad to receive.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.