It truly depends on the port and the activity. You can do a search of the boards for independent tours and get great info from people who have cultivated great relationships with people like Captain Marvin. Just keep in mind....if you book a shore excursion on your own, the cruise ship will not wait for you if you are running late. They will wait for those who have booked tours through the cruiseline. I know this firsthand because we booked Stingray City through Carnival and we were over an hour late for the ship's departure time from port. However, the ship was there waiting for us when we finally made it to the tenders.
Perhaps you should list your ports of call and someone can give you specific information regarding independent tours that they may have tried. Good Luck!
edited to correct Captain Marvin's name!