I swear I can't find any good animes like attack on Titans.
Some that I've seen and LOVED:
1. Death Note
2. Code Geass
3. Deadman wonderland (fucking amazing!)
Most Helpful Guy
You seem to like more complex/sophisticated animes. Here are more good in that style:
Steins Gate (Thriller with time travel and a hidden terror organization, with a funny side character)
Full Metal Panic (Action school romance comedy but with hidden terror organization developing in background, in near future they are releasing a new season I am waiting for, already read all 12 books of it because they only animeted the first 4)
Higurashi no Koro Ni (Psychopatic horror thriller with MUCH blood and you see people going crazy and want to know the reason but every answer gives you new questions)
Erased (time travel thriller, rather serious compared to Steins Gate)
Psycho-Pass (futuristic cyberpunk action thriller)
Shinsekai yori (From the New World) (post apacolyptic thriller in a parallel universum, highlights the personalities and you start to notice how the world around is a lie)
Danganronpa (15 pupils can't leave the school until they find who of them is the murderer and every night one of them is killed)
No game No life (2 siblings land in a fantasy land which they need to safe by winning games against their enemies. Cheating is allowed unless you get caught. Funny, with many complex strategies for winning)
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Most Helpful Girl
I never saw Attack on Titan, but it has that kinda 'humanity in peril' vibe, right? I'd recommend:
Neon Genesis Evangelion
^ everyone knows this one, one of the best anime ever made, put anime giant GAINAX on the map, etc. It has a similar 'supernatural forces attack a heavily defended earth' theme, gets kinda into body horror & bio-machinery, and has one of the best stories ever told. It's cliché to rec NGE but I still gush about it idc
^ another GAINIX series, after Evangelion. It's reallllyyyyy good though, it's very silly and fun and has huge monsters also. And mechs!
^ this is veeery much in the disasterworld vein, really interesting story and like, Bladerunner-y cyberpunk theme. Some eps are just mindblowing, one of my faves.
Ghost in te Shell
^ another 'duh', but you need to see it. Watch the two movies! The series if you're really into it - it's good, but not quite as good. If you liked Ghost in the Shell, the director made an absolutely phenomenal film called 'Angel's Egg' you might wanna track down. It's an avant-garde art film, maybe not your thing. But it's life-changing.
Serial Experiments Lain
^ you probably won't like this but I'm gonna recommend it anyway. It's an experience you need to endure at least once in your life.
^ I've never actually seen the anime but I hear its good. The manga is fantastic. One of the best stories ever told, and Casca is my hero. And it has huge, gross monsters - the manga moreso than the anime. Major warning for child sexual assault, though - but in my opinion it handles it well.
^ this one is a fucking mess lmao. I don't... necessarily recommend it? It's interesting, it's fun to watch, it has a LOT of fanservice (you can decide wether thats good or bad), but it's also sort of the opposite of Berzerk in that it depicts CSA graphically and honestly not tastefully. bring a vom bag. But this is the most similar to the ones you've already listed.
^ this one is SO good. It's not really similar to SNK in theme but it still has a feeling of vulnerability etc. that is really potent. Essential viewing.
^ another duh, I know, but it has themes that might interest you as an SNK/Death Note fan. It's also just one of the best films... like, ever.
I hope that helped a little! Good luck!2