Honestly, other than shows that go seriously off-model (like tehcookie's post; Kyoani did a much better job with Kanon's art when they got around to it), I only find a couple off-putting. Mostly...well, One Piece. I willingly concede that the story is great, but the artwork took some serious getting-used-to; I just didn't like Eichiro Oda's character stylization. Same for Shaman King, which looks similar.
Other than that, I can go for almost anything. That's just the only type that seems like a "trend" (i.e. more than just one artist's distinct style).