Guys, lets be a little more careful? Spin is not an intrinsic angular momentum, as in something orbiting a point at a certain speed. No, as far as we know (unless there's been something new in the last couple of years?), the angular momentum analogy breaks down because the electron is, to the best we can determine, a point particle, meaning that r in r-cross-p is zero. (The relevant result is that an electron would have a rotational speed at it's "equator" in excess of the speed of light, which just shows that there some limitations to treating it as a particle in the classical sense.) We've left the classical world behind.
Nonetheless, we can continue on because of the formalism -- the rules are still good because they no longer explicitly call for some value of "moment arm" as if this was a mass on a stick turning around a point. In the quantum world, we can come up with rules that describe the quantity that classically is called angular momentum: the commutation relations. And the crazy thing is, (sweeping a ridiculous amount of detail under the rug) when you use those rules in the framework of quantum, you get a value of angular momentum comparable to the classical value. But, and the important thing here is, they are not classical mechanics. So we can investigate and see that there are other quantities that obey these some sorts of commutation rules. Spin was originally called intrinsic angular momentum, in part because there was an analogy available between the classical and quantum mechanics, and this weird quantity obeyed the rules for the quantum version of angular momentum. However, there's no classical analogy to spin -- it's not like the earth orbiting the sun while turning on its own axis, unless you want an earth whose radius is zero.