Haibane Renmei was directed by the one of the key animators of Lain, and shares it's character designer. It's very good, if a bit slow and existential.
Kino's Journey (2003) was also directed by Lain's director, it has a similar surreal feeling but I think I like it a bit better than Lain because it touches on things like politics and identity.
Other posters have already given good recs (I'll vouch for Paranoia Agent and the rest of Satoshi Kon's work), but if you're willing to change the genre to fantasy Mushishi is really good and also contains that same kind of thoughtful mysterious vibes.
The most relevant quote from the article. Emphasis mine.