 If you liked
Haibane Renmei
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 ...then you might like
Shoujo Kakumei Utena
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These two series have different look and feel, yet they take you to the same depths and heights. If you believe that Utena is just about sword-fighting or weird relationships or runaway kangaroos, just skip this recommendation. However, if you're into the spiritual/mystery layer of Utena, then welcome to the town of Glie for another bunch of shockingly right questions and answers. Likewise, if you're a Haibane fan in search of another mind-blowing story of true Friendship and Forgiveness, then Ohtori Gakuen is waiting for you (if only you don't mind some sword-fighting / weird relationships / runaway kangaroos).
The settings are drastically different, but they share some crucial aspects:
Main cast is about two girls, one that is naive and tries to find her place in the world and other that is more serious, introvert and with tons of hidden pain, the relationship between Reki and Rakka seems pretty similar to the relationship between Anthy and Utena, although the later is closer to a romantic one.
Secondly, both series are psychological, heavy on symbolism, are character driven, involves dialogue and open many questions that aren't explicitly answered in any of the series.