Just to echo everyone else here, FMLA is unpaid, but it is usually run concurrently with a paid benefit, like STD. Not all companies offer that (and they're all different- for example, where I work, it's 6 weeks at 100% pay and 6 weeks at 50% pay).
You only receive STD pay for yourself, too. If you take it for a parent, spouse or child (the other things you're allowed to take it for), it is almost always unpaid (unless you have a really generous employer).