We have had many of these experiences.
Our most recent on the 5 night Wonder from San Juan to Miami, my husband and I (traveling without children), were sat at a table for 10! We had the greatest time with 4 other couples (who were all traveling with no children). It was so interesting talking to each couple and learning about their
Disney Cruise experiences. We shared all of ours and I can say, every one of them had a story and we learned so much. We rotated around the table nightly, sitting by new people. We had second dining and I can tell you that the service was a little slow, as a our servers had a few other tables and it seems we were always last. We were never in a hurry, so it didn't bother us. We saw many of these couples on excursions and around the ship at other events. It was the best experience.
Our experience in Norway, last summer, we travelled with our 2 children and we were sat at a table for 8 with another family, with children around the same age. We also learned that they were from the same area as us - Southern California. It was very positive. Near the end, the kids were all sitting at one end of the table and we were able to talk to the couple face to face. It turned out very well. Our son attends college near them and has an emergency number!
In the Mediterranean, summer '14', we were traveling with our children and got sat at our own table for 4. Our kids made friends with some other children, sitting close to us, and there was swapping going on! Our kids went and sat at their table while the parents ate at Palo one night. We still keep in touch with this family.
We have sat as a party of 5 with another party of 5. Kids loved meeting others and seeing them around the ship.
I can say that Disney is very accommodating. If you ever want to change dining times, or table, you just talk to your head waiter. You can change on the first day when you get on the ship at a central location.