I'm not sure if it's exactly what you had in mind, and you might have already seen it, but in terms of under-appreciated anime I would put Planetes head over heals over anything else. If you ask me, that show is pretty much the definition of diamond in the rough.
Planetes is pretty well known and well received.
Ah... let's see.
Mushishi is one of the best shows of the 2000s and was pretty much ignored by a good amount of the population. It's really slow paced, and there really isn't a continual story, but the adventures of a "mushishi" and the people/communities he encounters. Mushi translates to bug for the most part. Mushi in the series are spirits in the shape of bugs(for the most part) that do different things according to what kind. Most of them change things to seemingly normal events, but how the stories are told and how everything happens is just amazing.
Seto no Hanayome. It's kinda strange that this isn't that popular. It's your non-typical harem series. It's about a boy who is saved by a mermaid, and is forced to engage her so that he is allowed to live/return to the normal world. The premise sounds typical and stupid, but it's more or less a plot device and not the main premise. To expand... the mermaid is the daughter of a Yakuza boss, she has a mermaid rival whose father is (to simplify) the Terminator. They are childhood friends with a mermaid guy who... just watch it... seriously. It's one of the funniest series I've seen, and it's anything but typical. Haruko Momoi does the voice of Sun, that alone is worth it.
Manabi Straight. Slice of life-ish. It's about a group of five girls who go to highschool. It's set in the future, where growth is slowed down, so they look like lolis. It's a really cute and amusing show but it is kinda typical. It is one of the better of its genre though.
Futakoi Alternative. It's a lot better if you watched/played the original Futakoi but it's not needed. Futakoi is typical galge turned anime, but the shtick is that every girl is a twin. Alternative is more about coming to age, and how we lose sight of a lot of the things we hold dear, and how simple thoughts and actions really make life worth living. It's very calm and easy going, and pays homage to A LOT of cultural things from around the world (the op is a parody of like 15 different US movies).
Honey and Clover. If you watched Higashi no Eden/Eden of the East, it's the same art style. This is once again, a coming of age story, but the characters in this are amazing and how everything unfolds is just poetically beautiful. It really really really portrays how people are, and how people have wants... but that doesn't mean they match the wants of others. It'll make more sense as you watch more into the series. There was a live action of it as well, which wasn't nearly as good, but still pretty good. I was really surprised this series didn't pick up more hype than it got, because it really is just good.
Off the top of my head, that's all I can think of.