What circulated coins are worth more than face value?

Dimes, quarters and halves made before 1965 were made of silver so those sell for higher prices. Look through A Guide Book of United States Coins (It should be available from your local library.) and you will discover that many coins have collector value in less-than-perfect condition. Of course, most of these have already been taken out of circulation by collectors and are unlikely to turn up in your change.