The Night Circus

Jonathan Strange and Mr. Norrell by Susanna Clarke. A battle between two rival magicians vying for power and prestige, set during the baroque Victorian period and coated in flowery language. This is probably the closest recommendation I have for similar books to The Night Circus.

The Prestige by Christoper Priest is a remarkable novel. You've probably seen the movie, but have you read the book. Two stage magicians battle it out, trying to one-up one another with more and more elaborate tricks. Like the Night Circus, it features a conflict/contest between two magicians, but this one is not played out in a circus but across stage halls. The conflict becomes deadly.

The Golem and the Jinni is a beautiful and poignant character about two characters who are forced together by circumstances. It has the same sort of feeling as The Night Circus, though more character oriented.

Lev Grossman's fantastic trilogy. An entirely more depressing, postmodern take on the fantasy genre, but there's a school setting for the magically gifted.

Ah Harry Potter. Is there any fantasy fan who has not read it? Not at all the same type of story, but there is a magical school setting and students of magic. If you are looking for this, then Harry Potter is your book, though an entirely more juvenile story and with poorer writing. 

The Sorcerer's House by Gene Wolf has the same sort of feeling of mysteriousness, magic -- and subtle danger. This time it's about a magical house and two children who stay there.

The Troupe by Robert Bennett Jackson. Mysterious, magical, beautiful. These are worlds that describe this masterpiece. It has somewhat of a similar feeling as The Night Circus, but the magic here with both books featuring a company of performers where the performances are magical. On that note, if you want mysterious and strange, also read Robert Jackson's American Elsewhere.