I am (re) watching Serial Experiments Lain, and I would totally recommend it, especially to people who like Sci Fi, Cyberpunk, shows that have more depth and complicated elements than most (in my opinion) and psychological even. If you are what some might call a "causal watcher", you probably aren't going to want to invest in this anime.
The show centers around a young girl named Lain (holyshitnoway), who is pretty much a loner. One of her classmates commits suicide, and a few days later Lain and her classmates begin to receive messages from the deceased person on their phones etc. Lain begins to respond to these messages, and her dead classmate tells her that even after dying she has been able to pass on into "the wired", and has found God. The anime then gets a bit more complicated and throws a shit load of theories and such at you which result in mind fuck.
Personally I love the animation and find it unique and of very good quality, however, since this show was first aired in 1998, its quality is not as good as what you would see being aired today which is to be expected. (And the opening is fucking amazing don't even get me started)