I'm gonna take some leaps If you like the mind games parts of death note (since you seem to like the first part) I recommend trying Kaiji. My personal fav and one that got me changing my expectation of anime. If you like DBZ I assume it's the fighting. And even though the first assumption is people who like Anime probably will hate sports , sports anime are usually just tournaments for battling. If you want superpowers, I might recommend Kuruko No Basuke. I you want Mind Games, maybe One Outs. If you want something more modern, Haikyuu is a good shout.
A general shounen? Fate/Zero is pretty safe to try.
When it comes to recommendations, realistically there are lots of great anime movies to give yourself more context for what to watch
- Ghost in the Shell
- Akira
- Castle of Cagliostro
- Kara no Kyoukai
- Nausicaa Valley of the Wind
These are all just based on what you've mentioned but they're still a lot of spectrum for anime you could enjoy but haven't tried