Just be careful if you book an excursion on your own (not through the cruise line). I don't have any personal experience on this, but have heard (and I'm sure many others will attest to this)...
Your medical insurance will not cover injuries if they occur on a non-cruise line shore excursion.
If the tour is late and you miss the boat, it is your responsibility to get to the next port. If an excursion booked through the cruise line is late and you miss the boat, the cruise line in resposible to get you back onto the boat (at their cost).
If you are OK with taking these risks for the cheaper cost, then by all means, go for it. There are plenty of cruisers that do non-cruise line excursions and have not had any issues.
Star Princess - December 2006
Adventure of the Seas - April 2005
Caribbean Princess - July 2004
Golden Princess - March 2003
Disney Magic - October 1998