Our typical Disney trip might be no more than 4 to 5 Disney major parks although we spend 11 to 12 nights in the Orlando area. We won't go to a park on our arrival/departure day. Hubby likes to do a park every other day to make things less hectic. We enjoy the night extra magic hours, so if you are staying out until 2 to 3am at Magic Kingdom, you are in no shape to go to a park the next morning. On our non-park days we have gone to a water park, Fort Wilderness and Hoop De Doo, visit the monorail resorts and do a character meal, shopping at the outlets or Downtown Disney, relax at our resort swimming or spending time in the DVC community hall, go to a Universal Studios park. This works well with our non-expiring water park and more hoppers that we used to like to purchase. If we are going with other families who don't like to spend as many days in the area, we still only go to the parks 4 or 5 days but go every day and might add on a couple of more relaxing days at the beginning or end of the trip. Our upcoming trip in March will be one park per day Sun-Wed, Thursday might be a water park, Friday is a Universal Studios day, Saturday we might go back to Magic Kingdom because it is an extra magic hours late night, Sunday will be a relaxing day, probably at the resort or Downtown Disney, then we fly out early Monday. We haven't gone on a Disney area trip where we didn't go to a major park at all but we have considered the idea of taking a budget trip and just visit water parks on our non-expiring ticket.
Or at least we succumb pretty easily; while we had a great time our last Disney vacation, some of us really regretted not doing more "resort" days (which for us include hitting Downtown Disney, watching the fireworks from the Poly beach, etc.). Right now our plan for next time is to get a party ticket at Disney, and then a two-day ticket a Universal, and call it good (we'll be there eleven days or so). With younger ones it may be easier for you to do half days, though, so even adding days could be pretty restful compared to all day, every day in the parks.