A priori knowledge is knowledge before or despite experience. But as such, does this not either mean or at least entail innate knowledge?
I think Jo's answer is right on, but I just want to draw out the differences a little.
innate = from birth <=> adventitious = arriving from outside
a priori = without experience <=> a posteriori = derived from experience
All innate knowledge is a priori, but not all a priori knowledge is innate.
All a posteriori knowledge is adventitious and all adventitious knowledge is a posteriori.
Plato advocates that we have innate knowledge of the forms. Neo-Kantians (19th century) really liked Kant and seemed to equate the two but most contemporary Kantians thinks things like "there is an a priori form of right action" (at least that's how I read Korsgaard), but they do not think this is innate. Rather they think it's what happens when you apply the idea of action.
Descartes also considers innate vs. adventitious ideas in part of his proof for God's existence but to my knowledge he does not use the terms a priori and a posteriori -- though many people understand him in these Kantian terms.
Taking ideas and working them together is to yield a new idea synthetic . Learning something by breaking down a known complex idea is analytic.
Here's an interesting page that uses these terms correctly (or at least how they are used in contemporary philosophy).
All knowledge of mathematical propositions is a priori, i.e. you do not need to make experience to prove it. Such mathematical statements are "The sum of angles in a plane triangle is 180 degrees." or "Infinitely many prime numbers exist."
Mathematical knowledge is analytic: Alone from the meaning of the terms triangle or prime number one can derive these statements. Therefore mathematical knowledge does not need to make experience like science.
Nevertheless this knowledge is not innate. Each generation has to learn how to prove these mathematical propositions.
The terms "a priori", "analytical", "a posteriori" and "synthetical" as characterization of different types of knowledge play a prominent role in Kant's theory of knowledge, see the first chapters of his "Critique of Pure Reason".
His main point is the existence of synthetical knowledge a priori, e.g. that every event has a cause (principle of causality). As far as I know, Kant did not equalize a priori knowledge with innate knowledge, neither analytical nor synthetical knowledge.
Kant's claim on the existence of synthetical knowledge a priori is highly debated and refuted by many philosophers.
A typical proponent of innate knowledge is Plato with his theory of forms. He uses mathematical knowledge to show that we have quite a sophisticated knowledge already from birth; see his dialogue "Meno".
One possibly useful example to hold in mind is Chomskys notion of grammar as an inate idea: we aren't born speaking French, English or Bengali - we learn it, surely; but our knowledge or understanding of how grammar works, Chomsky holds is inate - it's for this reason he expects there to be a universal grammar - for surely any man could conceivably learn any language.
An example of an a priori idea, is that 2 + 2 is four; again this is something we learn - I remember learning how to add numbers - but when we understand why it's true, we find that it's true not contingently (because of experience, like this blue cup before me is coloured blue - for I can imagine it otherwise) but universally - which has a family resemblence to Platos theory of forms or of universals - it's this universal character that is called a priori.