Yes, both the cave tubing and the stingray city tours are "musts" for those port stops. I have not been to Roatan yet but for Cozumel, you must do some form of snorkeling or scuba. At the very least hit a beach. There are many things to this nature that can be done "on your own" or even with a ships tour. In Cozumel, one of the Mayan ruin tours is nice but that consume the entire day. If it is going to be your first time in Cozumel, you may want to skip those in favor of seeing Cozumel and save them for a future visit.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007