LovesToRun - I read your posts about how you are planning to balance your port days. My thinking is very similar...kids are 17 and 6, and I've been trying to figure out how to keep everyone happy. We, too are planning a few port intensive days, with lots of history (Rome, Ephesus), balanced with some really laid back port days where we just do our own thing and explore what the kids want and go back to the ship when they are tired. I know they would be bored to tears if I drag them through church after church and it is their vacation too.
Since I've been doing all of the planning and homework, we're going to have an evening dedicated to each port before the trip where I'll tell them all I've learned, watch some videos - maybe even some themed food from the different countries for supper that night. I figure that if everyone knows what is ahead of us, and some of they history behind it, that they will appreciate it more when we go. Plus it will help us all get even more excited.
We took them to NYC last summer, and it was very hot on the day we went to the 9/11 Memorial. We left there and went on the Staten Island ferry to get a look at the Statue of Liberty. I was showing my then 5-year-old where to go to get a look at the statue, and he looks at me and says, "Mom, you know I don't really care about any of this, right?" We ended up getting off of the boat and going straight to McDonald's, of all places, for ice cream. The funny thing is that now whenever we talk about New York, or he sees anything on tv about the Statue of Liberty, he gets all excited and talks about how he saw that. Even though we were all cranky and hot at the time, it's one of the stories we talk most about from that trip. I expect we'll have some similar stories after our cruise.
I think that is so smart to spend time before the trip to talk about each port/city with the kids, watch videos, explore the food, etc. We have been doing the same thing here.... it is really international here in Seattle, and we have lots of ethnic food restaurants around. So, we are going to start going out to Greek, Turkish, French and Italian restaurants to experience the cuisine (well, we already have our favorite Italian restaurants, but we'll be finding some good Greek, Turkish and French restaurants).
It's funny how kids are, too. They really are little "sponges", but don't always admit it, or realize it. My kids do the same thing.... they may not seem as interested in something, but later on, it will come out somehow about how they had a certain experience, or visited a certain place, etc, and be excited about the experience that at the time they didn't seem as interested in. I'm sure there will be times on our Med cruise where our kids will complain, but like you said, this is a vacation for our entire family, so that is why we are making sure that we are doing something at each port that the kids really want to do, too, and then it can be really enjoyable for all.
I just think this is such an amazing opportunity for all the kids who will be on our Med cruise (and adults, too!).

And, after our trip, in school in their history classes, they can speak from experience when they have units relating to the history they experienced on our trip.

When we went on the Panama Canal cruise Jan 2011, since they missed school, their teachers asked both our boys to keep a daily journal on the trip, and then write a report and give a presentation in their class to all the students after they got back on the Panama Canal. At first, our boys complained that they had to do all this extra work, but they ended up getting really into it, and in the end, they both learned so much from the trip on the Panama Canal and they were able to share their experience with their classes. It might be for all the kids on this Med cruise, at some point in school, they can use their actual experience in what they saw and places they visited in a report or project at school, and it'll make the project lots more fun since they experienced it first-hand.
Also, I think it'll be great for all the kids to meet, too, on the cruise... I'm sure friendships will be made.