I'm just in the middle of watching a pretty amazing and highly-regarded anime. It's called "Monster", it's very interesting, the story is so good it feels like watching a movie or reading a book rather than watching an anime.
There's also the new anime Aku no Hana that's being aired, the anime is special and interesting because it's rotoscoped, but the manga is a lot better in my opinion. It might look very weird and disturbing/creepy (which you might like) at the beginning, but slowly it becomes.....Very interesting =P I don't want to spoil anything but I recommend to try it, it's really amazing.
Another anime I've finished watching is "NHK ni Youkoso!". It's pretty amazing and I think many here can somewhat relate to it. It has funny parts, sad parts, the music is pretty awesome and I enjoyed watching every episode. To be honest the first time I read the description to this anime I've thought "Mehh, sounds boring and like stuff I've already seen before." a couple of months later someone recommended it to me saying it's really good, so I gave it a try and I'm very glad I did.