This was our 9th cruise sailing with Royal Caribbean and the Independence is one of the best ships in their fleet. My husband and I went for our 13th wedding anniversary and we were treated very well. From the second we arrived they gave us special discounts and small gifts (cookies, fruit, robes, etc), which made us both feel very special. Even the excursion we had in St Kitts with Thermon Grey (http://www.thenfordgrey.com/The_Tour.html) was spectacular and a must see if you go to St Kitts.
Even at dinner, our waiter and assistant waiter saved us a special desert for our anniversary, since we went to a specialty restaurant on the actual day of our special day.
I hope that if you enjoy Royal Caribbean, you take the Independence. Their staff if great! Friendly and very willing to help you in any way.
The only drawback would be that when they had "adult" shows on the cruise (comedy, game shows, etc) they did not enforce their 18 and over policy. Instead they backed off some of the adult themes. Now I understand wanting to protect the children (most of which were teenagers), but this is at the expense of other customers who went to the specific event because they were adult themed. RC's game show "The Quest" for example, the cruise director skipped over an activity because there were children in the room.