Black Hat : techniques or tactics which have been defined by Google as in violation of the Google "Quality Guidelines" . The Black Hat label applies to those methods specifically mentioned n the "Guidelines", other methods and/or tactics or circumstances mentioned by Matt Cutts in his blog, in Matt's comments on others' blogs, or just about anywhere anyone from Google says anything that strongly suggests Google took action against a site for some specific reason. Black Hat SEOs know what they are doing is defined as BAD, and do it anyway for specific reasons (not usually including "get banned"). I like to think of Black Hat SEOs as opportunists. They see an opportunity to gain, and take it, managing the associated risk. Please don't confuse ignorant SEOs with Black Hat SEOs... the ignorant ones are those who execute on Black Hat (evil) tactics without managing the risks (either out of ignorance or folly doesn't matter to me here).
White Hat: techniques or tactics which can be defended as NOT being contrary to the spirit of Google's expressed quality desires, by citing Google's own published guidelines, Matt Cutts' blog posts, or comments posted in other places, or just about any other Google communication. I like to refer to White Hat SEOs as "conservatives" of the SEO world... where things are viewed as BLACK or WHITE (GOOD or BAD), and the letter of the Google god is taken verbatim as TRUTH. Yes, there is a bit of a timeline problem with that approach (if Matt said it was bad in 2002, is it still bad?) but that's just the tip of the White Hat iceburg.
Grey Hat (or Gray Hat): Since the color gray is between black and white, logically Grey Hat SEO sounds like a label for the middle ground. But it's not. Because White is pure white and grey is a shade of black, we have confusion. Some say Grey Hat is NOT White Hat and is just a shade of Black Hat. So let's step away from the coor wheel and define Grey Hat as the practice of tactics/techniques which remain ill-defined by all that published material coming out of Google, and for which reasonable people (not White Hat SEOs, mind you, but "reasonable people") could disagree on how the tactics support or contrast with the "spirit" of Google's published guidelines.