Martial Arts Masters is a new Facebook that sees you in charge of your very own dojo. You'll train your fighter, buy items to strengthen them up, and enter them in challenges against other opponents. You can even fight against other players. This all takes place in a largely text-based game where you manage filling meters a lot more than you do actually fighting.
Destiny Stone is one of the most extraordinary games on Facebook. It completely eschews Facebook's love affair with timer-based management sims to offer players a 2D side-scrolling platformer with combat, RPG stat progression, an equipment system, and an item crafting system as deep as anything you'd find in a console game. There's even a story-based plotline to follow with characters you can recruit and optional little dialog sequences to unlock. Where most Facebook games expect you to pay for the right to play it for hours on end, Destiny Stone is content to let you play as much as you like.