Most people at least try to dress "pressed casual." You get a few tourists in jeans and t-shirts, but I'd say the most common broadway outfits are sweaters and blazers (with a smattering of suits) for men, and casual dresses and slacks/blouse/sweater outfits for women. Women can get a bit dressier--particularly with their outerwear. In the winter I see tons of fur coats outside the theaters. But rarely true formalwear (i.e., tuxedos and evening gowns).
My personal favorite are the high school tour groups, who are clearly given "dress code" instructions for their Broadway visits. You'll see busloads of 'em going into theaters in the evenings--all the boys with shirts and ties (but no jackets) and all the girls in casual dresses or nice slacks with blouses or sweaters.