Watched on Netflix Deathnote and Full Metal Alchemist: Brotherhood. Now I just finished Steins;Gate - need a good new one.

Bleach

There are lots of good ones besides those, but I need a bit more information to narrow this down.

Are you only looking for shows on Netflix?
Have you watched any other anime besides the ones listed?
Those three are all pretty different from one another, do you have a particular genre you enjoy more than others?

Preliminary list of shows you can't go wrong with

Action

Claymore - Violent as all hell and beautifully animated.
Berserk - A classic anime that doesn't even scratch the service of its source material unfortunately. Watch the old one, the new one with the terrible animation is shit and then pick up the manga if you have to know more.
Attack on Titan - Ongoing but near it's conclusion supposedly. One of the most praised shows of the past decade, it's an exceptional watch
Hellsing Ultimate - The MC is my all-time favorite bad ass anime character.
Fate/Zero - A lot of people rag on fate, but this installment was exceptional. MCs backstory alone makes it worth the watch imo.
Fate/Stay Night (Unlimited Bladeworks) - If you enjoyed the other one, it's good to watch this as well. The rest can all be skipped, they suck.

Psychological/strategy

Monster - This show is fucked up, no other way to describe it. You just gotta watch it.
Code Geass - Genius child with a grudge against the ruling dictatorship is given the power to do w/e the fuck he wants. Mental battle back and forth between MC and his opponents lead to some awesome moments and a great ending.
Future Diary - Another fucked up show. I don't want to give anything away.
Gantz - Slightly dated and a little pervy, but it does capture the hormons of teenage boy in a horrendously fucked up situation pretty well imo.

Shonen

Hunter x Hunter 2011 - The best Shonen anime, far better than Bleach, Naruto, One Piece, Fairytale etc...
Yu Yu Hakusho - A bit dated, but still an entertaining show. The English dub is unbearably bad, stick to Japanese for this one
Black Clover - Ongoing, pretty damn good
My Hero Academia - Ongoing, pretty damn good

Misc

Megalobox - Sports anime, insanely entertaining and short)
One Punch Man - Comedy, make sure you've watched at least a few of the popular shonens before watching this, it'll make it so much funnier.
Samurai Champloo - Comedy/Samurai action - A fucking classic, a must watch for everyone who likes anime
Cowboy Bebop - Space cowboy bounty hunters with a comedy aspect, another classic that should be watched by all anime fans.

Since you listed a strategy + psychological show and a shonen I gave a decent amount of those and then I threw in a decent amount of solid action anime.

Boku no pico

Bleach

Not just Netflix shows, I just got a two week trial last night on this site funimation, has a fair number of shows and English dubbed.
Only watched the shows I listed, along with a few episodes of One Punch Man.
For genre, I'd prefer stuff like Deathnote and Steins;gate

I'll check some of the ones you listed. Buddy mentioned Code Geass

Death Note is one of my all-time favorites, it's hard finding others like it.

There's a new season of Steins out as well, I just haven't watched it yet, so I couldn't recommend it. If you like dark though, Monster and Future Diary are both pretty fucked up. Code Geass is mecha, which turns a lot of people off, but aside from moments of being lighthearted, it's the closest to Death Note imo.

Death Wish >

Yeah Death note was so damn good, made me like anime, but like you said hard to find others like it.

Future diary was pretty good haha and can vouch code geass is amazing and a must watch