I've found in many cases that I'm not a huge fan of anime. Rarely does it capture me in such a way that I have to watch the entire series. In particular I dislike a lot of the action-based animes which feature an overpowered main character, not only does it make the action depend entirely on that character but it also takes away the tense element of action sequences. In addition I've found more and more that I can't really deal easily with the main characters of anime. In particular I find myself drawn away from teenage characters.
That said, I am a massive Miyazaki fanboy to the point where I have designs in the works on a Miyazaki-based half-sleeve. It is at that point, though, that I have to acknowledge that Miyazaki, and Ghibli in general, I find, avoids the anime tropes that I struggle with and become annoyed with. In certain ways I don't regard Ghibli films as anime because of this.
In terms of my favorite anime series, I've been captivated by three series to the point where I watched them in their entirety. Cowboy Bebop and Samurai Champloo were two such series, but neither so much as Claymore. Claymore doesn't have the best story, but I love its characters, and it has a lot more heart than I see a lot of anime putting forth. It's also important to note that, as an anime, they focus on someone who is the weakest in a world of incredibly strong peers. It's the only anime that has ever gotten me interested in manga, as well, and for that I'd say those reasons Claymore is my favorite anime.