Also, since you've watched Lain, I also recommend Haibane Renmei. I would also like to add Paranoia Agent, as well.

Legend of the Galactic Heroes, not necessarily symbolism heavy or anything but it's a very thoughtful and intelligent series with a large cast full of some amazing characters.

Apart from what has already been mentioned, I recommend Angel's Egg. It's a movie with minimal dialogue, very strong imagery and highly surreal.

Princess Tutu has a lot of the same elements of Utena and does a brilliant job at desconstructing the magical girl genre.

Ergo Proxy is a dark sci-fi anime full of so many cultural references and surreal moments that it is rife with rewatch value.

Odds are you have seen it already but if you haven't the second Ghost in the Shell movie is full of mind fuck and beautiful to behold while keeping up the density of the franchise.

Mugen no Ryvius is another self-conscious post-Evangelion anime that really pays it homage without being a clone. While not as surreal as some of the titles already mentioned it is one of the most realistic takes on the 'teenage mecha pilot' trope. Imagine Lord of the Flies in space, if you will.
Very much along the same lines, Texhnolyze. It gets increasingly less narrative as it progresses. It also makes Eva seem cheerful.

Mononoke is a super stylised take on traditional Japanese lore. Very beautiful, dubious main character, each arc is a mixture of bizarre symbolism and sheer brilliance.

And speaking of surreal, try Cat Soup. It is not deep in any way (I think, I am actually not entirely sure) but it is so utterly surreal that it deserved being mentioned here.

I would like to add The Tatami Galaxy to the mix - it's a festivity of trippy animation, visual metaphors and surreal plot, even if it is dealing with everyday themes (student life and maturing).

In case you need something a bit lighter to freshen your palate after the more serious and heavy stuff.

And to borrow satyr's song rating system, this anime gets ( Meh but ok | One of the most beautiful things EVER )

Perfect Blue and Millennium Actress omg

Everyone's already recommended everything I would! I honestly can't think of anything else so symbolism-heavy, but if you like to think, Ghost in the Shell is always a good one. It's more like philosophy than psychology, though.

If you're willing to stray from anime, Hannibal has some excellent symbolism (but super-gory, so watch out).

The Tatami Galaxy and Shin Sekai Yori were both on my list of "other things to recommend if these aren't enough."    I left off Tatami Galaxy because the OP specifically mentioned deep psychological analysis of the characters, and I don't think Tatami Galaxy supports that.  But symbolism?  Metaphors?  Motifs?  Hell yes.  You have to be patient, though.  It all comes together in the last couple episodes.

As for Shin Sekai Yori, that one is... utopia/dystopia, growing up, being different.  ( none | 6 )

Everyone's already recommended everything I would!

I love screwy surreal anime. I'm sad that it's barely produced anymore. The most recent ones would be Madoka Rebellion and Yuri Kuma. And Despera will be coming out eventually, but other than that...

Thanks for the suggestions guys!  I also heard that Radio City Fantasy, Kaiba, and Mind Game are good in this regard.

Pale Cocoon is more meditative, than anything, but I think it's an wonderfully potent meditation. And very pretty.

I may be alone, but I can't help but feel that Mamoru Oshii's work tends to be less revelatory or thorough, often, than what he's basing his work on, when it comes to adaptations. Ghost in the Shell and Beautiful Dreamer, for examples, have some great moments, and a nice, strong tonality to them, but they're incredibly pared down from their source material and to me.

I really enjoyed watching Ergo Proxy.

I can be a little pretentious and up-its-own-ass but definitely has that surreal, psychological edge to it. My favorite episode is one where the characters get stuck and stranded - spending the entire episode doing nothing.

I recommend:

1. Ghost in the Shell
2  Wings of Honneamaise
3. Spirited Away
4. Death Note
5. Gilgamesh

I watch numbers one and two every year because they are technology based anime.  The other three I like because of the social and spiritual overtones.