Do sit-ups really work for firming up your belly?

Part of program. Sit ups can help tone the abdominal musculature, but it will not get rid of the fat over the muscles. There are several layers of muscle that run in different directions. It is helpful to do different sit ups that target each layer.
Crunches better. True sit ups actually focus more on exercising your hip flexors. Crunches or similar exercises focus more specifically on working the abdominal muscles and thus help firm up the belly area.