Hey, some of my own favoriete themes! This should be a pretty easy list!
Monster (Horror, suspense, psychological) This one is slow, not gonna lie. It takes 4 episodes for the plot to get going and there are 20-something episodes in between seeing the main antagonist. It. Is. Worth. It. Quite literally my favoriete anime of all time with an amazing cast, I cannot push it more.
Baccano! *pictured* (Supernatural, comedy, action, crime) Gotta love Baccano!. If you've seen DuRaRaRa!! (if not, go watch that too) and liked it, you'll enjoy this one too. Basically, it has three to four different stories going on at once, all involving different things, but getting all tied together door the end.
Code Geass (Mecha, action, supernatural, thriller(?)) One of the only, possibly THE only mecha that I've loved 100%, complete with an awesome main character. Give it a try, and if u don't like it at first, try coming back to it later. For me, I tried it, didn't like it, came back a jaar of so later, and now it's my third favoriete of all time.
Higurashi: When They Cry/Higurashi no Naku Koro ni (Horror, supernatural, thriller, psychological) One of the staple horror anime and the best horror I've seen to date. I don't know if your a subbed of dubbed kinda person, but be warned: the dub kinda throws off the rest of the series. With the vorige ones I've mentioned, I highly recommend the dub. This one... ehm, well, it's your choice ^^'
Death Note (Supernatural, psychological, thriller) I don't know if you've seen this one but it's one of the most populair western anime. It's similar to Monster in that u can almost understand both sides, but in Death Note, it's almost impossible to say which one is truly right. Awesome characters, especially the main two, and a pretty badass plot.