Being more into tv drama than comedy, there are only a handful of characters I truly love and the very first one that came to mind after reading this thread is Reverend Jim Ignatowski of "Taxi". I just loved that character.
Week after week, and with him being only a co-star, I waited for the sometimes only one hilarious line, but he kept me in stitches. The kind of character you just look at and crack up (hence, the picture I posted)
TIS