There were several commercially and critically acclaimed musicals since The Producers, some of which ran longer as well (Jersey Boys Avenue Q and Hairspray spring to mind). The Producers holds the Tony record, which will make it something of a landmark production, but it mostly limped along after Broderick and Lane left. Then the movie bombed. I didn't care for it, but I can see why people thought it was funny. I'm not sure if it will be the "last great classic".
Also, I'm not convinced a "classic" is defined by critical and/or commercial success. West Side Story divided critics and Follies has never had a profitable Broadway production. Like them or not, I think the last "classics" we've seen on Broadway were Rent, Ragtime and Hairpsray with The Lion King, Jersey Boys, Mamma Mia, Wicked and Book of Mormon being noted as popular blockbusters. Honrable mentions go out to Urinetown, Avenue Q, Caroline or Change, Light in the Piazza, In the Heights, Spring Awakening, Grey Gardens, Drowsy Chaperone, Spelling Bee, Next to Normal and Once. That's not my order of preference, but rather how I see them being noted in the history books.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian