I'm going to put forward a slightly more qualified version of Curmudgeon's response and suggest that there is no one-size-fits-all answer to this issue.
I've seen cases where a way-off-the-beaten-path solution is funny, poignant, thought-provoking, instructive, corrective, and/or otherwise worthy of reading. I've also seen solutions that qualify as vote-baiting detritus with no place on a serious puzzling site.
I consider 'abuse' to be cases where all of the following conditions hold true:
the solution lacks any true wit; these are precisely the hackneyed answers Emrakul was talking about
the solution egregiously violates the unstated assumptions in the problem
the "quirk" in the solution belies the necessity of most/all of the information given in the problem statement
'Abusive' solutions earn my rare downvotes, especially in cases where a question is replete with them, and especially if the solution is a one-liner that could be a comment instead.
Off-the-beaten-path solutions earn my upvotes if they succeed in intriguing me, making me laugh, or otherwise entertaining me. I'm not going to hold off based on some puritan notion of always-colour-inside-the-lines quality standard.
Any solution that's neither here nor there I leave alone.