My favorite would have to be Cowboy Bebop hands down.
I enjoy all genres of anime. if you take a look at my "currently watching" list you will see a wide variety of titles. The first anime I ever watched was the VHS version of Princess Mononoke, and the first series I ever watched was Gundam Wing. I am a big Gundam fan, mostly UC timeline. That and I am a huge mecha genre fan, it is my top genre for watched material.
I have just started picking up reading Manga again, so no clear favorites yet. I have really enjoyed Shingeki no Kyojin, and Full Metal Panic Sigma.