I can recommend Princess Tutu that hasn't been recommended yet.
The Fate/ serie is pretty swell to, however, there is different ways how you should start watching/reading the serie, just start somewhere that isn't made by Studio Deen.
You have probably seen Neon Genesis Evangelion been reccomended many times on other sites (and maby here). While I think it's an OK serie (the TV serie and EoE movie), I hate the majority of that fanbase (pls, don't become a hardcore fan and start bashing people becous they don't think it's the best serie ever made and etc.). btw, if you havn't watched evangelion yet. Pls, watch Gunbuster first (only 6 episodes). I think I don't know anyone that saw Gunbuster before Evangelion. Could be interesting.
I also recommend Eureka Seven, keep in mind, AO isn't a sequal. Don't watch AO unless you see it as a spin off serie.
Monster (not Musume) is a must IMO.
You could also check out Death Note, I only recommend the 25/26 first episodes however. If you want to watch the rest then sure. but it will probably be your only time then.
Code Geass is a favorite of mine. My biggest complain about it is some BS reasons in season 2 (and the pizza fillers).
Hunter X Hunter (2011) is one off THE best shonen battle series ever created. However, the ending might be very unsatisfied.
And while speaking about Hunter X Hunter, I think Yu Yu Hakusho is still good today.
I think I'm done with series now.
You should also watch movies. Ghibli is ghibli, you will most likely like them all (except Earthsea). Then we have the "mantatory" movies "you must watch", which are Akira, Ghost in the shell, Paprika, Perfect Blue and some more I forgott. And I'm soo sorry I havn't watched it yet, but I think Redline is also a must.