How long you should stay at Disney World will depend on your budget and how you like to holiday. Walt Disney World alone spans 4 theme parks, 2 water parks and a shopping district. While on the surface you could set aside a day for each park, you'll likely need longer if you want any time to relax - but that's not to say it's not doable.
The deciding factor for how long to stay at Disney World is your budget. While we like to go for at least 2 weeks, some people may only be able to budget for 1 week. We're not "hotel snobs", so we'd happily stay at Pop Century for 2 weeks over Wilderness Lodge for 1 week. We would also think it's better to go for 2 weeks every other year than 1 week every year. However, budget comes down to what you can save and what you want to save.
To save money, some people stay off-site. Hotel prices outside of Disney can be significant cheaper and it allows families to stay for 2 weeks at the cost of staying in Disney for 1 week. While you don't get the benefits of staying on Disney property, and you'll be required to do a bit more travelling around, it can add more days to your stay for the same money. The plus side of staying off-site is also the flexibility to do non-Disney things.
Our General Guidlines
If you're staying at a Disney World resort hotel, you will need to stay at least 1 week but preferably 2 weeks depending on your budget. If you can only budget for 1 week, you will still be able to enjoy most experiences. However, it can feel quite rushed. 2 weeks is the sweet spot because you'll be to do pretty much everything once, what you really love a few times, and have times to relax in between. 3 weeks is my favourite, where you can really do everything as much as you want with plenty of time to chill out in-between.
Like To Stay It Slow?
Staying for 2-3 weeks allows you to holiday at a slower pace like we do and enjoy using our half day tip. Where you go to one park in the morning, go back to the hotel around lunch time to chill or go to the pool for a while, then head out in the afternoon and evening to another park. It allows you to go to a park and do a portion of it, and then do the other portions on other days. It feels a lot less rushed and you get the feeling of walking up Main Street U.S.A. multiple times rather than just once or twice if you stay a week and do a full day at a park.
It is very exhausting to try and do a whole park in one day. Ideally you need at least 2-3 days per park. The perk of staying in a Disney hotel, as said above, is you can go back to the hotel after a certain amount of time, chill out, and go back later, at no extra cost (as long as you have the Ultimate Ticket).
Length Adds Flexibility
Staying at least 2 weeks also gives you flexibility for when Florida's weather tries to ruin your holiday. If you planned to see Fantasmic and it gets cancelled due to weather, then it's not too hard to fit in another night.
While you can still have a great time going for a week, it's always worth staying a little longer for 10 or 14 days. Even more so if you plan to go outside of Disney to do other parks or to do some mall shopping.
We like to stay for 3 weeks, but usually stay 2. We do stay for 3 weeks if the prices are favourable, which differs from year to year. 3 weeks is really nice because it feels like you're there for a really long time. It's really nice after being there for a week you still have 2 weeks left. It's something you can't quite grasp until you've done it.
It comes down to how you like to holiday and how much budget you have to play with. I think if you're going for a first time and can afford it, save the extra and go for 2 weeks. Don't underestimate how sore your feet get and how hot it get can - you'll want times to chill out.