 If you liked
Serial Experiments Lain
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 ...then you might like
Mawaru Penguindrum
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Two highly detailed anime's in which unassuming youngsters uncover they are actually part of a massive conspiracy which unfolds as the series progresses.
These anime's are very similar in content, yet being that both are mystery, it's difficult to put forward why they are alike without incorporating spoilers, so once you give this pair a change, this recommendation will make a lot more sence.
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Recommended by Gleam_Queen
I'm surprised there aren't that many recommendations for these two.
Some of the biggest links are extremely spoiler heavy, but overall both shows explore inherently abstract themes while relying heavily on their strong direction and symbolism. Both shows also utilize their main supernatural-esque gimmick in very unique ways, operating beyond the realms of the logical world.
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Recommended by DeadlyChuck314