Weather is an important factor to consider when visiting Orlando, but if you are heading the theme parks, you should also consider the crowd factor in making your decision on when to go.
Fall and Winter
A good time to vacation in Orlando is September or October. It is still very warm but far less humid. With the kids back in school, the crowds at the theme parks are much more manageable and there are plenty of seasonal celebrations in October. At the Magic Kingdom, there's Mickey's Not-So-Scarey Halloween Party (great for kids) while Universal Orlando hosts Halloween Horror Nights (great for teens and adults).
The weather tends to be very nice in November, but note that many schools in the Northeast U.S. get a winter break in early November, leading to heavier than normal theme park crowds.
Early December (about the first two weeks of the month) is a very nice time to visit. The theme parks are all decked out in their holiday decorations and holiday events, but the crowds do not show up until the end of the month.
The crowds can be so heavy during the last two weeks of the year for Christmas and New Year's that the theme parks have to close their doors (or at least their parking lots). So avoid these two weeks if at all possible. A better option would be to go earlier in December if you are looking for the holiday decorations and events.
If you spot a person wearing shorts in Orlando during January, chances are pretty good it's a tourist. Locals will be wearing long pants and maybe even a sweater or jacket. The good news is that even in the middle of an Orlando winter, the weather is pretty good--chilly to locals, but plenty warm to people who visit from cold weather climes.
Spring and Summer
The do-not-blink-or-you'll-miss-it spring season in Orlando (March-ish) is an okay time to visit weather-wise, but the theme parks are likely to be overwhelmed by crowds of families on spring break from school.
The summer months (June-August) bring high humidity, afternoon thunderstorms, and masses of hot and sweaty tourists.
If you absolutely must go in the summer, then plan on waking up as early as possible and hitting the theme parks as soon as they open (stand in front of the gates and wait if you must). The early jump on the day will help with both the weather and the crowds a bit, and if you plan your day right, you can get out of the park before the thunderstorm hits and go for a late lunch, take in an afternoon movie, or do something else indoors (like DisneyQuest or a walk around the atrium of Gaylord Palms). It is definitely not recommended to spend the entire day out in the summer sun and heat.
If your skin is not used to the intense Florida sun, be sure to wear a hat, sunglasses and sunscreen. And consider bringing a rain poncho for those afternoon cloudbursts. The theme parks sell them, but at a very inflated price.
Hurricane Season and Rain
Florida's hurricane season runs from the start of June until November with the worst months being from late August until October. It can be really humid and the time of the daily thunderstorm is not as predictable as June's 3pm downpour. Staying during this time may mean losing a day due to severe weather or cancelled flights. However you could just get a rainy morning which makes people avoid the theme parks.