if you're just starting out and you like sci fi and thrillers i would suggest:
Code Geass- similar to death note (which is also pretty good) but with sci fi, mechas, and a superpower that lets the protagonist control anyone he wants by looking them in the eye. Because of the superpower thing, the series has some intense chess-like mind games (also like death note).
Steins;Gate- there's not much i can say about it since its easily spoiled, but just know that its about time travel and despite it starting out really slow, it gets AMAZING later on (around episode 10-ish)
Cowboy Bebop- space bounty hunters and jazz music, thats all you need to know. its also really good for people who are new to anime since its very western in style and it was made by the same people who made Space Dandy...so theres that
Death Parade- a psychological thriller that tackles the value of being able to live a life and the suffering and joys that it comes with.
Fate/Zero- Fate Zero is REALLY REALLY REALLY good. just....just watch it. it has amazing animation and characters and also has a thriller feel to it
also even though you may not want to read any manga, Naoki Urasawa's Monster is one of the most intense psychological thrillers i have ever seen. there is an anime adaptation but its almost impossible to find
What follows is all just my personal opinion.
My biggest suggestion, rather than paying attention to any particular show, is to try out a variety of genres and see which of those you like most. Granted, there are some shows that transcend genres, but there are some things that you'd never know you'd love them until you try them.
Some genres to consider:
*Long running shounen
Psychological / Psychological thriller
Slice of Life
*Asterisked "genres" are technically demographics, but are so rarely catered to that they may as well be genres
Etc. You can look around for specific recommendations in each genre, and fans of the genre are more likely to tell you some of the best shows. For example, i'd be rubbish at giving you action or mecha suggestions, but would be quite good at giving you slice of life, idol, or josei suggestions.
Even if you think "I probably won't like this genre", I think most people are surprised at what sorts of things they find. Anime is quite a diverse medium, after all.
But that's just my personal suggestion, of course.
These series in my opinion are some of the best in their genre while also being decently short. (12-26 episodes.)
I've linked where to watch them. Check out the synopsis and see if anything interests you. Unfortunately most are from funimation, not here on Crunchyroll.
Sakamichi no Apollon
One Punch Man
Gekkan Shoujo Nozaki-kun
Shingeki no Bahamut: Genesis
Steins;Gate since you enjoy sc-fi, dramas, thrillers, and mysteries
Gankutusuou: The Count of Monte Cristo...the animation may turn you off, but it's a great anime with an amazing villain.
Serial Experiments Lain-
Eden of the East
Kids on the Slope
JoJo's Bizarre Adventure
You may find some you like among these. I tried to stick to the genres you enjoy. These can either be found on CR, Funimation, or Hulu
I'm Not Really Here Anymore. Nothing Personal. Will Try To Be Semi-Active
Knights of Sodnia
good judgment comes from experience,and experience comes from bad judgement.
Here's a few recommendations:
Fate Zero http://www.crunchyroll.com/fatezero
One Punch Man
Virginity best girl
If I marked it in red, it means to my knowledge it is not or no longer on CrunchyRoll.
I enjoy mysteries, sci-fi, dramas, and really dry comedies. I enjoy thrillers as well since they're generally mixed with mysteries. I enjoy a good adventure as well!
Adventure: Fullmetal Alchemist（There are two versions：Fullmetal Alchemist and Fullmetal Alchemist: Brotherhood), Akame ga Kill, Bleach, Dungeon ni Deai wo Motomeru no wa Machigatteiru Darou ka(Is it Wrong to Pick up Girls in a Dungeon?)、Fate Series(Fate Zero/Fate/Stay Night)、Hitsugi no Chaika(Chaika the Coffin Princess), Hunter x Hunter, No. 6, Zetsuen no Tempest(Blast of Tempest)
Comedy: Wagnaria(Working!!), YuruYuri, Yurushiki, Ore no imouto ga Konnani Kawaii Wake ga nai(Oreimo), Ouran High School Host Club, Nisekoi, Midori no Hibi, Maria Holic, Kokoro Connect, Kill me Baby, Danchigai, Denki Gai, Anime de Wakaru Shinryounaika(Comical Psychosomatic Medicine)、Aiura、Mikakunin de Shinkoukei(Engaged to the Unidentified)、Ore Monogatari(My Love Story!)、Shinryaku! Ika Musume(SquidGirl)、Watashi ga Moutenai no wa Dou Kangaitemo Omaera ga Warui!(Watamote)
Drama: Clannad, Chuunibyo Demo Koi ga Shitai(Love, Chuunibyo and Other Delusions), Bokura wa Minna Kawaisou(The Kawai Complex Guide to Manors and Hostel Behavior)、Ao Haru Ride(Blue Spring Ride), Angel Beats, Inu x Boku Secret Service, Isshukan Friends(One Week Friends), Kami nomi zo shiru sekai(The World God Only Knows)、Kamisama no Inai Nichiyoubi(Sunday without God)、Kimi ni Todoke：From Me to You, Love Hina, Maji de Watashi ni Koi Shinasai!(Majikoi)(Please Love Me, Seriously), Puella Magi Madoka Magica, Nazo no Kanojo X(Mysterious Girlfriend X)、Ookami Shoujo to Kuro Ouji(Wolf Girl and Black Prince), Plastic Memories, Sankarea, Shoukugeki no Souma, Shigatsu wa Kimi no Uso(Your Lie in April), Soranowoto, Sukitte Ii na yo(Say, I Love You), Tasogare Otome x Amnesia (Dusk Maiden of Amnesia), Tonari no Kaibutsukun(My Little Monster)
Mystery：Gosick, Another, Gokukoku no Brynhildr(Brynhildr in the Darkness)、Durarara!, Jigoku Shoujo(Hell Girl)
This is a pretty big list for a beginner, so sorry about that, but maybe you can see what a few of them are about and see if any interest you. Happy watching, dude!
Shingeki no Bahamut: Genesis
The Heroic Legend of Arslan
Tiger and Bunny
Jojo's Bizarre Adventure (2012)