I'm all for any anime that eschews cliche. Very few (if any) can avoid them all, but there are probably quite a few that manage to sidestep the big ones. See how many animes you can name that avoids each of the cliches below (not one anime that avoids them all, as some are genre-specific). If you can think of any I missed, suggest your own as well.
A fantasy anime that doesn't involve some kid from the "real" world crossing over into another world.
An anime where the lead man and woman have a good in-story reason not getting together.
A fighting anime where the lead hero has a love interest who doesn't passive-aggressively slap the shit out him for comedic effect.
An anime where a government agency hunts down a specific enemy (say, vampires or demons), but doesn't have a team member that is related to that enemy (a half-vampire or a half-demon).
An anime where the supernatural investigators don't have some cute, made-up name for whatever it is they hunt (i.e. Aragami, Hollow, Chiroptera, Methuselahs).
An aime where we meets the hero's eventual love interest in an episode other than the first.
An anime with energy-wielders (ki, chi, spirit energy, etc) where the lead hero doesn't have deep, untapped reserves of raw power that surprise everyone around him.
A fighting anime that doesn't have an abrasive tough guy who eventually becomes a lovable second bannana.
A "robot suit" anime where the lead pilot doesn't have severe emotional hangups (at least more than any non-robot-pilot anime hero).
An anime with an old man character who has no perverted tendencies.
An anime where the hero defeats the main villain of the series by being smarter, not by being stronger or better-skilled. (And by smarter, I don't mean devising the perfect laser beam attack or something)
An anime where the bad guy wins.