Hohohoho, best under rated anime you say? Hohoho, what kind of genre you like to watch? I mostly go for the green side (the lily side) and female protagonist type of anime.
Here's the few I could name:
Rinne no Lagrange - Mecha/Friendship (Threesome, for my google eye

(you need some imagination to know it ;3)). It got 24 episode and it was kinda fun for me, on the mecha part. Very well made anime and the characters kinda funny too for me. It's bout intergalactic fight that for some reason drag Earth-san to the middle of it (tho it only happened at Japan, how sad).
Bodacious Pirate Space / Shin Mouretsu Pirate - Bloody awesome underdog anime and it got movie to boot! Both are super good and I wish they make another season, alas, it wasn't popular. They are pirate, a _space_ pirate y'know? The crew is super wholesome, and it got some side lily character on the side. The Protagonist got nice pace of maturing and think rationally. The animation was very well made for that year too.
Muhyo and Rouji : Supernatural Investigation Bureu - This one is a shounen type of anime. Got enough horror and a whole.jargon of goodness too. It got nothing to do with the genre I usually go, but ey, it retain it own original storyline and that worth to watch.
Toaru Kagaku no Railgun series - A
WHOLE LOT BETTER than the main story goes. The girl doesn't go dumb each time they interact with the f male protagonist, that is for sure. Highly recommended since it's action pack and well made animation


The storyline got some connection to the main but it got its own too.
Yama no Susume - Slice of life goodness and a bunch of girls going for mount climbing. That's it, fuwa fuwa feeling is a hit.
There's another magic law-ish anime but can't remember it. It had 12 episode and its a female protagonist. There's like slight mecha magic involved and it's super awesome anime with a well made animation too. Lh well, can't remember it since I already delete the whole thing. I watch alot of anime and there's a long list of it but eh, Imma recommend what's still feels good to rewatch to u xD