Noah and the Tower Flower, an Irish play with Irish actors.
Jack Perry is Alive (and Dating), a musical with a highly questionable plot for which one of my friends had written the music.
Chinglish, a very good production brought to Broadway from the Goodman in Chicago. It's protagonist is an American businessman going to China to sell local municipalities signs in English with correct (i.e. unembarrassing) translations. The protagonist is really just a foil for the Chinese and for a Brit living in China. Quite funny. It annoyed me when the BBC reported on the play as being a "Broadway" play without mentioning that it had originated in Chicago.
Any Given Monday, an excellent quirky, philosophical play at 59E59 which was not about football (American or otherwise).
Dona Flor y Sus Dos Maridos, which I attended under false pretenses. My mom got me to agree to see this play while my parents were in town without me realizing that it was in Spanish. I don't speak Spanish, nor do either of my parents, at least not well enough to follow a play. There was a live translation, not that it would have mattered much: the play was rather nonsensical.
The Dumb Waiter, a Pinter play about two hitmen waiting for an assignment from their boss. (Why is this such a common concept for plays?)
Other Desert Cities, which was amazing. I wanted to go because it was staring the excellent Stockard Channing (from The West Wing) and because it had good reviews from its earlier staging at Lincoln Center. It was a traditionally excellent play, so excellent that I am shocked, shocked, that it's probably only the fifth best play I've seen so far this year.