Because Greed is Homunculus, he has the power of regenerating from any attack possible. Even if his core, a Philosopher Stone, is completely taken out, he can regenerate his whole body in a couple of seconds. This goes, however, at the price of some energy that is drained from his Philosopher Stone. It does take a while for the Philosopher Stone to wear out, but when it finally happens, Greed can be permanently killed.
He has the "Ultimate Shield" this ability allows him to make alter the atomic bond between his carbon atoms giving him impenetrable diamond hard skin. Despite this his shield is slow and can be 'outran' meaning that his body can only generate it at a certain pace. This doesn't mean he can't cover his body, which does if he needs to. This makes him practicly invulnerable to any physical damage. If Greed covers his hands with this, they turn into claws, which are sharp enough to cut through rock and steel. Since he is a homunculus his is vulnerable to alchemy and his Ultimate Shield can be inverted turning into the most fragile form of carbon possible. In the 2003 anime this is how Edward ultimately defeats him.
Since the second, and most known, Greed shares the body of Ling Yao, with Ling himself, Greed can switch with him who the control of the body has. And if Greed is in control, Ling is still able to give Greed advise. This is a clear advantage, since Ling is an excellent ninja, and was able to figure out Wrath's blind spot within seconds. Ling's ability to sense Homunculi also came in very handy, when they had to fight Gluttony in complete darkness.