I do explore on my own. But things like Dolphin swim and Swim with the sea lion were not offered on their own or was too difficult with transportation and simply easier to to book with the ship.
I also book with local venders, I try to get the most out of my shore days and I always research the ports and activitys. If Im in a tender port such as Belize and doing a 7 hour excursion I will book with the ship, the ship will wait for people on their excursions to return but your out of luck if your on your own, your ship could sail away without you.
In Nassau I took a city bus to Arwak Caye the Fish fry area where the locals eat and had a great lunch at a beautiful spot with no tourists, and then walked to the Zoo, Ardastra gardens to watch the flamingos march and feed the parrots, we took a cab back to town, still had time to shop for jewelry and rum cakes it was the best day of that cruise.
Carnival Mardi Gras 1987 (Bahamas)
Carnival Legend 2005 (Exotic Western Caribbean)
Costa Mediterrenia 2005 (Eastern Caribbean)
Carnival Pride October 2006 (Mexican Rivera)
Carnival Legend 2007 (Western Caribbean)
Carnival Glory 2009 Western Caribbean
Carnival Liberty 2011 Eastern Caribbean
Norwegian Spirit 2011 Western Caribbean
Carnival Miracle 2012 Southern Caribbean