In no particular order:
M.A.S.H.
Cheers
Trick - Just brilliant all the way around. The professor who lacks common sense and the clever but ill-fated magician teaming up to solve mysteries. Sounds kind of campy, sure, but the humor is so skewed and different and the characters are ALL eccentric. I especially love how everything always goes wrong for the heroine. It was extremely popular, with 3 seasons and several movies and OAVs.
Keizoku 2: SPEC - Another off-kilter series. It has a lot of dark comedy but it's also serious and sometimes bloody. The male lead is a no-nonsense cop who was buried in the unit for dead cases as part of a cover-up. There he meets a highly eccentric detective and begins to fall into a web of conspiracy involving people with impossible abilities. Erika Toda is absolutely incredible as the female lead, a genius with a bad attitude and many personality defects.
Spongebob
Are You Being Served
