Can someone explain the leagues to me?

I know of normal and hardcore, but I saw something about cut-throat leagues...

What all leagues are there?

I know:

Normal: nothing special... you play through the game.

HC: play through the game, but if you die your character dies.

cut-throat: what is this?

Any others?

Normal: nothing special
Hardcore: if your character dies, it goes to normal (it's just a "never die" ladder)
Cut-throat: you can join other people instances of maps, kill them. You get XP from killing them and all their inventory including equipments.

Normal and Hardcore leagcy: cf Normal and Hardcore. For characters made before big balance changes.

There will be a few more leagues with different rules, and different rankings. You'll be able to make your league with the people you want and the rules you want, in the future (however it'll have a cost).