St. Brigid's Church in the East Village spent several years in a stare-down with the wrecking ball after it was closed by the archdiocese. The building, in fact, was almost torn down when a demolition crew showed up in 2006. But an anonymous $20 million donation allowed for the building's repair, and the church finally reopened this weekend. EV Grieve has photos and the Times has some building history.
Here's the demolition/renovation progress c. 2009: