TheMadNode said:Must watches on you're list are:
-Another
http://myanimelist.net/anime/11111/Another
-Claymore
http://myanimelist.net/anime/1818/Claymore
-Death Note
http://myanimelist.net/anime/1535/Death_Note
-Kokoro Connect
http://myanimelist.net/anime/11887/Kokoro_Connect
-Psycho-Pass
http://myanimelist.net/anime/13601/Psycho-Pass
These are from you're list, I went alphabetically so my favorites out of these are Death Note, Psycho-pass, Claymore. But don't get me wrong, all of them are superb.
Here are some other must watches that aren't on you're list:
-Clannad (Romance, slice of life, drama)
http://myanimelist.net/anime/2167/Clannad
-Darker than Black: Kuro no Keiyakusha (This one is overlooked a lot)
http://myanimelist.net/anime/2025/Darker_than_Black:_Kuro_no_Keiyakusha
-Densetsu no Yuusha no Densetsu (Really good but ends on a cliff hanger)
http://myanimelist.net/anime/8086/Densetsu_no_Yuusha_no_Denset
-Fate/stay night (I found this one better than Fate/zero)
http://myanimelist.net/anime/356/Fate/stay_night
-Fullmetal Alchemist: Brotherhood (Top 3 of all time for me)
http://myanimelist.net/anime/5114/Fullmetal_Alchemist:_Brotherhood
-Great Teacher Onizuka (Action, comedy, drama, school)
http://myanimelist.net/anime/245/Great_Teacher_Onizuka
-Guilty Crown (One of the best endings I've seen)
http://myanimelist.net/anime/10793/Guilty_Crown
-Hataraku Maou-sama! (Really fresh and genuinely funny)
http://myanimelist.net/anime/15809/Hataraku_Maou-sama!
-One outs (Very well written but can be hard to follow)
http://myanimelist.net/anime/5040/One_Outs
-Shingeki no Kyojin (Please watch this)
http://myanimelist.net/anime/16498/Shingeki_no_Kyojin
-Steins;Gate (At the end I was speechless as to how good this was)
http://myanimelist.net/anime/9253/Steins;Gate
-Suisei no Gargantia (Very refreshing and nothing like some of the other mechas)
http://myanimelist.net/anime/16524/Suisei_no_Gargantia
-Sword Art Online (Not everyone's cup of tea, I really liked it though)
http://myanimelist.net/anime/11757/Sword_Art_Online
Sorry if I went over board on the recs. I hope you find something to watch!