I'll add my voice to those recommending both Azumanga Daioh and Urusei Yatsura and I'll throw in a recommendation for Irresponsible Captain Tylor as well. I know you asked mostly for 'random' type comedy and this one has an overarching plot, but I think it will be *very* much worth your time. I've never known anyone to be disappointed by it.
(Plus, it has *the* MOST awesome space battle *ever*!)
(Plus, it has *the* MOST awesome space battle *ever*!)