There's the Umbridge discussion that everyone has mentioned -- and while Snape can dice the truth fine as frog's hair, he's never actually lied by comission as far I can tell. He's actually disturbingly truthful, if highly biased.

So he has applied for the the DADA position repeatedly, and been denied. I do believe that JKR said that Dumbledore denied Snape the position with the idea of 'let's see how you do in Potions', too, which might have given Snape the idea that he could eventually get the job... which he'd be a diaster at frankly, because his students would be hiding behind their desks, even though he probably does know as much DADA as Lupin.