If you liked Lain, check out Texhnolyze and Boogiepop Phantom.
If you liked Mushishi, check out Kino no Tabi.
Other good serious anime (in no particular order): RAINBOW, Paranoia Agent (okay this one has a funny episode thrown in later but the rest of it is rather surreal, still aimed at an adult audience), Shinsekai Yori, Berserk, Ghost in the Shell (kind of mecha but mostly cyberpunk), Now and Then, Here and There, Kara no Kyoukai, Aku no Hana, and Ping Pong: The Animation (some of the characters in this show are wacky and crazy, and the animation and art style is quite experimental. It's a little hard to take it seriously sometimes is what I'm getting at).