- Gurren Lagann (Favorite anime of all time. Not really similar to what you've listed but it is an action series and it's VERY exciting. It's a really hot-blooded series and it's always inspiring. It's a mecha but it's not a typical mecha by any means.)
- Code Geass (Amazing and truly worth the hype. In my personal opinion it's even better than Death Note, but I'm gonna make it clear that Death Note and Geass really aren't THAT similar. The psychological battles are very different. Death Note is more about the wit battle solving the mystery before your opponent deal, but Geass is all about the strategic warfare and manipulating your troops to accomplish your goals.)
- Steins;Gate (Fantastic story. Starts off a bit slow but the second half begins a mysterious, complex plot and everything that happens is very compelling. The characters are used very well and the story is amazing to watch. The whole mystery thriller thing is very big in Steins, though there is little psychological warfare like in Death Note)
- Higurashi no Naku Koro ni (Amazing mystery. First season has a powerful horror vibe while second season is more about the mystery than anything else. A very haunting story that will keep you guessing and can disturb you at times, particularly in season one. In spite of how brutal and gruesome the series is, the characters are very lovable and you wouldn't believe it seeing some of the horrible things they do but the characters are very developed by the end.)
- Future Diary (Comparable to Death Note but with more action and less intelligent characters. 12 people have diaries that can record the future in different ways and must kill each other to become God. Very action-packed and some good wit battle strategy along with the fights, though many of the characters weren't as smart as they should be.)
- Neon Genesis Evangelion (Most psychological mecha I've ever seen. Starts off okay but the last quarter of the anime screws with your mind a lot and explores the human mind and the relationships of the characters in connection to this more than I have ever seen in previous anime)
- Mahou Shoujo Madoka Magica (Looks like a kiddy magical girl show, but don't be fooled. It's a dark, psychological story about how a simple wish can destroy your world and how good intentions can slowly destroy a person and sink them into despair. It's very well done but ends very quickly.)
- Durarara!! (Mystery-ish sort of show but it's hard to say what genre it is. You've got a huge cast and the anime explores just about all of their stories, it's interesting to see how they connect and learning the character's pasts as you continue on through the rest of the plot is really captivating).