Scotch (cellophane) tape. Apply completely around the finger covering the wart, and change daily. Covering them like that softens them with the retained warmth & moisture, and changing the tape pulls off a bit every time painlessly. Takes a couple of weeks or so to remove them completely. Sanitary and cheap.
For the more chemically-minded, acetone (nail polish remover). Apply a single small drop to the wart two or three times a day, no more. Slowly dissolves them.
Don't combine the methods - the acetone will eat through the tape.
In general, though, they will work themselves out. I used to have about three or four when I was a kid, and as I got older, they just simply went away.