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

Since I was a kid, I was told that some lizards can lose their tail on purpose for distracting the predator and make their escape, then they can regrow a new one no problem at all.

I am not sure how common it is.
What are some common pet lizards with this kind of regeneration ability?

Most reptiles I have seen have some ability to regrow some portion of their tail. Leopard geckos I know can regrow most of thier tail. I have seen bearded dragons regrow some of it. Far from complete. Most species of anoles and fence lizards can regrow most of their tail.

Do these reptile species you mentioned "drop" their tails on purpose?
Over a decade ago, one of my friend's brother had a lizard. Not sure what type of lizard it was. It was green, that's all I know.
One day he was panicking and told us his pet lizard had lost its tail.

Most lizards can do this. However, I wouldn't consider it a benefit of having that as a pet. Mainly because you don't want to make it lose its tail. It stresses the animal out, and the new tail is never as good as the original one. Be nice to your lizards. =P

What are the functions of a tail for a lizard?

When you say it is not as good as the original one, what does it mean? Not as good looking? Not as easy to use?

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.

Can bearded dragon and leopard gecko lose and regrow their tails too?