Usually I would say an ache could be described as a dull pain, that is, not neccesarily less painful, but a constant pain, usually from within the limb. On the other hand, "my knee hurts" could describe a sharp pain, or an aching pain.
It's difficult to describe, but I hope that helps you somewhat.
If you say "My knee aches," I would think that the pain doesn't result from any particular recent injury or event, but is (as zemirah wrote) an ongoing, probably dull state of pain, like from arthritis. "My knee hurts" would tend to make me think it's a sharper pain, and maybe (though not necessarily) the result of something specific that happened. But we're talking about nuances here.
I think that "ache" is a particular kind of pain, just as Elisabetta describes it, and that "hurts" is just another way of saying "gives me pain". "I hurt my knee" is different, though; it means that I injured my knee.
Hurt can be aching: "Mommy, my stomach hurts." "Mommy, I have a stomach ache." These are not kidspeak, and are legitimate sentences.
Patient: My knees hurts.
Doctor: Is it a dull, aching pain or a sharp pain?
I really do think (both as a person who has endured lots of surgery and lots of injuries, and as a nurse who who has treated lots of people) that "hurt" is a more general and less formal term for "having pain" and "ache" is a specific type of pain (dull, constant).