There are a few anime that I have seen that I enjoy dissecting and analyzing. I'm a literature buff, and I relish complex symbolism, extended metaphors, motifs and allusions. A few of the ones I've seen that have these are:
Revolutionary Girl Utena (mostly the series, but the movie too, I guess)
FMA (no really!)-The original, not Brotherhood. Not that Brotherhood isn't good, it's just not deep enough to warrant an introspective reading. Also, don't ask me to talk about The Conqueror of Shamballa. I honestly hate that movie too much to even make fun of it.
RahXephon (although I've only seen the first few episodes, I can tell, and I'd be happy to go ahead and finish the rest of the show if someone wants it explained. The same goes for Darker than Black)
GITS has a lot of philosophical allusions but those are really really freaking obvious so I doubt anyone needs me to explain those.
From what I've heard of Madoka Magica it would count as well, but I don't know where it's available and I don't like to watch things illegally, so that one will have to wait.
If you would like me to analyze an anime, or if you have questions regarding the ones listed here, please reply. I am ready to rise to your challenge! Also, feel free to put together your own interpretations of ones you've seen. I'd love to get a discussion going.