The Atlantic Cities blog examines why we don't see tons of dead pigeons in cities, even though we see tons of live ones:
Here's a brief accounting of all the ferocious animals that eat urban pigeons:
Red-Tailed and Cooper's Hawks: These stocky killers know that fat city pigeons have the juiciest meat. So they roost all throughout the states in trees, on roofs and atop telephone poles, waiting to take the birds “on the wing,” as Seerveld puts it. “In Orlando where I live, it's unbelievable,” he says. “They pick off pigeons like they're one of their favorite food items.” The wildlife expert recalls one time when an Aeropostale employee called him because a hawk was stalking a pigeon INSIDE the clothing store. “A pigeon flew in and a hawk chased it right through the door,” he says. “I caught it with a net and brought it outside and let it go.” Here is that hungry, hungry hawk.
Author John Metcalfe helpfully links to a few videos, including one of a hawk eating a live pigeon and a turtle moving faster than you ever thought possible.