It depends on what type of styrofoam and where you live.
Most packaging/shipping stores will accept clean styrofoam peanuts and reuse them. Reuse is just as good as recycling, these can be reused indefinitely.
Some recycle centers will accept specific types of styrofoam for recycling - mostly the type of styrofoam that is white shaped styrofoam like computer components are often packed in. Try googling your location and "recycle styrofoam" (for example - Texas recycle styrofoam - got 585 hits).