Tough decision, but if I actually have to choose one, my favorite show is probably Ano Hana. It's the only anime I've ever rated a full 10/10, which on my scale means that I have no complaints about it whatsoever. There's quite a few runner-ups, though. Steins;Gate, Perfect Blue, Nichjijou and Welcome to the NHK are up there.
My least favorite is easy: Shigatsu wa Kimi no Uso. I absolutely loathe that show. It's not even close to the worst anime I've ever seen in terms of quality, but I find it so repulsive on a moral level that I couldn't stomach sitting through more than, I think, five episodes. The way this show handled the topic of abuse is wrong in so many ways that I don't even know where to begin, and seeing how popular it is confuses me.
I liked Shigatsu wa Kimi no Uso overall, but it was manipulative and heavy handed in parts. The only part I really liked was in the middle when the MC mentors a younger piano player. I thought the abuse was over the top and weird, and even worse it was just a plot device, but if you stopped at episode 5 you didn't even see the worst of it.