Hammocks are cold, that is the biggest problem. You also can't really just flop down on one and lounge out the same way that you can in a bed.
From a totally utilitarian standpoint of "place for sleeping", a hammock has some benefits. It's small, it's highly portable (mine fits in my backpack), and it is pretty comfortable.
In reality, though, most people use their beds for a lot more than sleeping. Reading in my hammock is pretty difficult, so is using my laptop if I want to type anything. You can't comfortably fit more than one person in one (unless you've got a garden hammock with spreader bars on it).