Well since it doesn't matter what genre, I'll suggest the ones I likes the most myself. So you already have some of them in your list
For for starters I would recommend
Fate/Zero, a prequel to F/SN which is 20 times better.
Aria series - I'm usually not into episodic shows but this one was really good. IF you like slice of life and want to see something relaxing and calm, it is a great choice. If you are in hyper mood, stay away or you'll get bored
Series have interesting characters and some interesting stories. It gets better with each season. Origination is a real treat once you watch all other shows since it gives a rewarding conclusion. First season is called
Aria the Animation.
Series focus on new city on different planet that is similar to Venice. Main heroine wants to become a professional undine. Series follow her training and journey. It has both realistic and fantasy touch, almost like any Key work.
Bakuman - not my all time favourite but it has a lot of good stuff going on. Series are about 2 guys who wants to become professional mangaka. We get to learn more about manga industry and how things actually work there what I found interesting and unique. Right now season 3 is airing. Season 1 has a bit weak start but show keeps getting better.
Berserk - old series, won't be surprised if you already saw it. It is based in knight era. Series have interesting characters and story that gradually is building up for something big. 3 remake movies were released not so long ago. I have watched 1st one but to be honest old anime series are better so far.
Chihayafuru - awesome series that got many people by surprise. Just like majority I picked it up out of boredom but ended up loving it. Series are about Chihaya who has great passion for Karuta card game. Game on its own sounds boring but anime was able to give it so much depth that is hard not to get engaged.
Series have great animation, entertaining characters and engaging story. Really worth a try. Season 2 aired yesterday and so far seems to be the best thing of this season.
Claymore - action series based in knight era. Earth is full of human eating monsters and special organization has created special female warriors to haunt them down. Series have interesting animations style, entertaining characters and for me personally, engaging story.
FMA and
FMA: Brotherhood - probably best shounen series out there. Original FMA series have an original anime story whole Brotherhood is a remake that follows manga. Only several first episodes are the same. If you won't like FMA, still try Brotherhood since you might like different take on a story there more.
Ga-Rei: Zero - "Will you kill the one you love because of love?" series are huge mix of drama/comedy/action/horror. It starts with action, goes into happy flashback which eventually leads to a heavy final.
Yomi is one of the most memorable characters.
Ghost Hunt - do you like ghosts? Do you like detective stories? If yes, you'll love this one since it is both. Group of specialists are employed to investigate weird cases and find solution to them. Engaging story with engaging set up that keeps you at the edge of your seat, Anime is divided in arcs, each one follows different case. First arc is the weakest.
GTO - old comedy series. Main hero Onizuka is a perv who wants to become the greatest teacher in Japan. However, when things actually ask for it, he is very dependable and will help his students no matter what... though his kind of help is now what you would expect... like for example pushing your student off the bridge... did help!
Hmmm..
K-ON maybe? Slice of life shows where cute girls do cute stuff. No real fanservice, nice songs and pretty funny.
Kami nomi zo Shiru Sekai - a different take on romance/harem. Main hero is the biggest gamer ever and loves to play dating games. However, by accident he signs a contract with a cute demon and is forced to date girls' for real to get bad spirits out of them. If he refuses, his head will be cut off...
Funny romance/comedy with entertaining characters. Keima alone is a win.
I'll stop here for now. Will add more if needed
