What are some common pet lizards that can regrow their tail?

Well, it is not as attractive. The main purpose of the tail in most species, at least most people think the main purpose of the tail in most species, is fat storage. Energy storage for when there isn't as much food. Lizards are far more active than snakes and typically eat more and need more intake to survive. Obviously many species use their tail for balance as well, some will use it as a whip for defense, some arboreal species have what is pretty much a prehensile tail for climbing.