I could easily spend a week at Disney World, but only if staying 'on-site' on Disney property. If you do that, and you only do Disney, you don't need a rental car. There's the Magic Kingdom, Epcot, Disney's Animal Kingdom and Disney Studios as the main parks. I rate them in that order. Minimum one day each.
The Disney water parks are great, but really take a whole day to get in/out and enjoy
when they're open.
For Disney World questions,
www.wdwmagic.com and
www.mouseplanet.com are the best sites.
Universal's definitely a fun couple of days by itself, but rent a car.
Many hotels will offer a free shuttle service to Universal or Disney but for the aggravation of meeting up with it (their schedule vs. yours), it's really better to have a car.
If renting a car, the traffic in that area is nuts. I found it better to leave really early in the morning, plan to arrive at your destination about 7:30 AM, even if it means sitting in a parking lot quietly. Florida's warm, so the AM will be nice and the driving stress you'll avoid by leaving early will be well worth it.
It'll also assure you'll be at whatever theme park at opening in order to get your full value for the pricey admission tickets.
Most people there don't use turning signals and the idea of following the rule of pass on the left, keep to the right otherwise just never seems to happen.