Well as for me: There's so many Animes that I like that it's really hard to chose one, but I think my favorite Japanese Anime is still "Welcome to N.H.K" (NHK ni youkoso). Even though it's already some years old. I still think it's a so very great Anime.
From cartoons, there's also a lot that I have liked. Simpsons, southpark and etc. So it's hard to tell again, but I would like to mention a British cartoon "Kipper the dog" Although it's for little kids, I like it. Maybe I just like it because it's for little kids. I don't know. But It's a nice cartoon :)
There are also some nice British stop motions, that I like. Like "Wallace and Gromit". Well I think "Wallace and Gromit" don't need to include any video or pictures to introduce it here, it's so famous. :)