You might experience what I did, which was an inability to put the show down. Like I said in my long blog post about LotGH, it starts out pretty slow, but following the first season climax I was hooked. It's really good if you can get past the initial episodes (Which aren't bad mind you, just not as good as the rest of the show).
Speaking of things that are really good: "Seirei no Moribito".
This anime is basically my wet dream. It's got all the qualities of a good Samurai story, but without all the clichés that follow, because it's not actually a Samurai story. It follows a female warrior named "Balsa" whose past is a mystery to the viewer. All you're told in the initial episodes is that she "once took the lives of eight dear people" and she now works as a bodyguard for hire in an attempt to find atonement. She will not rest until she herself has saved the lives of eight people. This anime has a number of things that really sells it though, besides the "Wandering warrior haunted by ghosts of the past" trope.
Animation. It is fucking gorgeous looking. It's made by Production I.G. so it is not too big of a surprise that it looks good, but this TV anime has better quality than many animated films.
Setting. Even though it might look like we're on planet earth somewhere in Asia, we're not. This world has two moons and the culture that surrounds Balsa is a mishmash of Chinese and Japanese squished together to form something unique.
World building. I can't really explain this very well but there is something about the world of Seirei no Moribito that just makes so much sense. It's not an anime that spends literally entire episodes on exposition (See: Fate/Zero) but instead just makes it feel natural by the sheer detail put into the world that surrounds our heroine. It feels realistic, even though the show includes supernatural elements. You'd probably have to watch it to experience what I mean.
NO FUCKING FANSERVICE. NO DUMB LOLI DEMIGODS. NO STUPID "EMBARASSING" MOMENTS. NO "KONO HENTAI, ECCHI, BAKA"... So far anyway.
The truth of the matter is that I've only seen the first four episodes (4/26) of Seirei no Moribito, but with the way things are currently looking I will be very very very very very surprised if I find any of the stereotypical clichés that permeate Otaku culture in this anime
TL;DR: If you like medieval/martial arts/fantasy/samurai themed stuff, give Seirei no Moribito a try. I can almost guarantee you will like it.