chesskid.com: free or membership, for young kids under 10 and under USCF 1000. It's safe because of the limited friend function. Videos are funny for kids.
chess.com: free or membership, parent of chesskid.com. Videos are of good quality, and a lot of discussion. More social. Tactics Trainer is good.
chessclub.com (ICC): membership. Because of no free account, players tend to be more serious. Videos are of good quality. The interface is more flexible and powerful. Most teachers use ICC.
playchess.com: membership. Use chessbase interface. Has tactics training based on chessbase database.
freechess.org (FICS): free. Similar to ICC. No video.
lichess.org: free. Getting popular now.