7 nights makes for a pretty nice trip without rushing too much (unless you're going during a busy time of year). No matter how long you stay, you won't be able to see everything, but you'll be able to ride everything you want to in 7 nights at all 4 parks. This time we're staying 9 nights to have a more leisurely trip. We're 2 adults with no kids (well, actually our trip is 4 adults this time around). Kids definitely slow things down so I wouldn't want to do less than 7 nights with kids for sure.
Generally speaking, 2 Magic Kingdom days, 2 Epcot days, 1 Hollywood Studios day, and 1 Animal Kingdom day works out pretty well. Some folks might do 3 MK days and only 1 Epcot day rather than 2 and 2. The rest of the vacation time can be spent at Disney Springs (Downtown Disney), one of the water parks, at your resort, or finishing up your favorite park.