Watch out for people offering you taxi rides at any transportation center such as the Port Authority, Grand Central, or Airports. Though many are honest, some are illegally evading a taxi dispatcher or just trying to lure you to a more secluded spot for mugging. Read about one traveler's bad experience at JFK.
Do not deal with people who approach you on the street with some kind of a money making proposition, they are the ones who are most likely to try to grab your money and run. Example: Bag-of-Money Scam
Don't fall prey to people who ask to check if your money is counterfeit or stolen. This can happen in a scam like the fake ID sale scam.