There's some pretty good ones out from Type-Moon, they've got Shingetsutan Tsukihime (Lunar Legend), and Fate Stay Night. Tsukihime is a bit on the shorter side, but if you like Death Note you would really like Tsukihime. Its a darker themed (somewhat) and the fights aren't half bad. I didn't really watch much of Fate-Stay Night. But that's another popular anime from Type-Moon.
If you want some action though, I might reccomend Black lagoon. I've been watching the first few episodes and its pretty good, decent gun fights an such.
Or if you just sorta want an every day anime you could go with BECK. Its about a Garage band that wants to hit it big, that and the music is REALLY good.
I don't really watch anime too much though. Though, The melancholy of haruhi suzumiya would be a good idea for you if you like mind games. I would also say, watch it in the "Original, Broadcast order" for even further mind games.
