As most everyone else has pointed out, it depends. We stayed 7 days this last trip, then went to US for 2 days. That was are longest stay at WDW. We still didn't do many things (one visited one water park), but it almost felt like one day too many. We spent the last two days mainly repeating rides and shows we liked the most.
Take the advice already given and stay a little longer since it is your first trip. You will likely be overwhelmed (and very tired) at first.
If you like to stay at the parks all day (commando style) and your kids are older, you can pack more fun into shorter trips.
If you will be doing one or more water parks, you might want to add an extra day. We usually stop by DQ for a few hours on at least two afternoons, so you don't necessarily need an extra day to take this site in.
If your family prefers parades and shows over rides, you might want to give yourself extra time because it seems to take longer to arrange to see all the shows at each park. We often end up missing a show or two because we didn't have enough time.
If you think your family will want to carefully explore all the countries at Epcot, take in the movies, meals, culture of each place, you will need more time. You could easily spend 3 days at Epcot and still not see everything.
Here is what we like to do:
MK - 1 and 1/2 days
EP - 2 days
AK - 1/2 to 1 day
MGM - 1 day
Water parks - 1/2 day each
DQ - few hours to 1/2 day
DD - a couple of evening trips (allow more time for serious shoppers

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