Thinking taxis are the most dangerous vehicles on the road in NYC is a terrible mistake. Taxi drivers - no matter how reckless they may seem from the backseat - are generally quite alert and aware, and even if they tend to speed and cut in, they realize that running over a cyclist would not be good for them. They use their horns occasionally, but more as a warning or a heads-up. No, it's the buses that are the ones to look out for. More like forces of nature than mere vehicles, NYC buses move with impunity, regarding their lanes and stops as sacred ground. And God forbid anyone who gets in their way. Steer way clear.
Be afraid of buses. Very afraid.