I rarely take ship's excursions. While it's possible for STUFF to happen, it's also possible to get hit by a bus crossing the street to your tour.
Going off on your own, there's no question you need to plan well, and allow lots of time for returning to the ship. But often, you can have more adventure, and spend less money going on your own.
Just remember to have a credit card with you, in case you're flying to catch the ship <G>