I'm a native Floridian who grew up as an Army brat and never lived here until adulthood -- but I've lived here ever since. I live in suburban Miami, about 25 miles from downtown.
The biggest pros, IMHO, about living in Florida are the weather and the tax structure.
The heat and humidity that many mention is MUCH more of a problem in the Orlando area than it is on either coast. Here in Miami, we rarely get above 92 degrees in the summer, and there is almost always a nice tradewind blowing which makes it more tolerable. Eventually -- usually about September -- the humidity starts to wear on you a bit, but it's nothing like the weather in WDW. The summer thunderstorms can be quite fierce, and they require some adjustment.
Yes, we have a hurricane season -- June 1 to November 30. To be honest, every place on the planet has some kind of weather issue, and hurricanes are not really something we worry about much. We actually worry a lot more about hurricane insurance than we do about storms. (My State Farm insurance doubled this year and we're looking for alternatives.) If a storm comes, we just button up, ride it out, and go through a period of inconvenience. When both Katrina and Wilma hit us in 2005, we were without electricity for a total of 7 days (although some were out much longer with Wilma than we were).
Generally, the weather here is warm, and it's humid in the summer months. You adjust; it's no big deal.
Yes, we have bugs. And lizards and frogs who eat the bugs. And snakes who eat the lizards and frogs. And hawks who eat the snakes -- you get the picture. It's a lush subtropical landscape and bugs come with it. If you're really freaked out by bugs, don't move here. Or, you can do what I tell DD5 to do -- "Don't eat them." Our current wildlife adventure is we have a possum family who have set up shop in our yard. I'll be trapping and relocating them this week.
The tax structure is one of the things that draws many people to Florida. We have no income tax (it's prohibited by our state Constitution, and I can't imagine that ever changing).
Our local taxes come primarily from property tax, which is capped at 2 mills (1 for local government, 1 for public schools), so property taxes tend to be lower than most other places for comparable homes. Local governments also impose fees for things like Fire Rescue districts, water & sewer, streelight districts, etc.
There is a perceived fairness problem with a provision of our property tax law, called "Save Our Homes," which macman752 referred to. That provision says that homesteaded property valuations cannot rise faster than 3% per year, and that does lead to some inequities. My neighbor across the street, with a slightly smaller house than mine, pays more than double the taxes I pay because I've been here 10 years and they just bought two years ago. Due to a "portability" provision just passed, I can now take part of my "tax savings" with me if I sell this house and move elsewhere in Florida. The Save Our Homes limitations do NOT apply to part-time residents or commercial property. Your opinion of Save Our Homes is one of those "Beauty is in the eye of the beholder" things -- if you benefit from it, you love it. If you pay more than your neighbor, you don't like it. But eventually, everyone's tax increases will be moderated by Save Our Homes.
Most of our state tax revenue is generated by sales tax, which is 6% statewide. Some counties have additional sales tax (Orange County has an extra 1/2%, I believe; Miami-Dade County has an extra 1%), and many counties also have a "tourist tax," which is levied on hotel rooms, restaurants, bars, etc.
The good thing about reliance on sales tax is that you wonderful folks who visit us each year (about 85 MILLION visitors a year!) pay a high percentage of that. I think the number is about 1/3 of all sales tax is paid by visitors.
The bad thing about sales tax is that it is extremely cyclical -- as the economy cycles downward (as it's doing now), sales tax revenues fall off sharply. That leads to boom/bust budget cycles for the Legislature to deal with. By state constitution, our state budget must be balanced, so right now our Legislature is trying to cope with a drop in revenues of more than $4 Billion in FY 2008-2009. It's going to be ugly and painful, and both state and local governments are going to be forced to make some difficult decisions.
Another good thing about Florida (IMHO) is that our state government has a tradition of being clean, open, and progressive. Florida's Sunshine Law, for example, has been a national model for open government for as long as I can remember, and it's extremely unusual to have a corruption issue at the state level, regardless of who is in office. We just worked through a corruption problem in our state Corrections department, but that was an individual problem, rather than a systemic problem.
Most issues at the state level are decided on a Floridian basis, rather than Republican or Democrat depending on who is in power. We have many more conflicts between North Florida and South Florida, and between urban counties and rural counties, than we have between political parties at the state level. (They fight like cats and dogs in national politics, but that's what they're supposed to do!)
Local governments are another story, and we've had significant corruption problems here in Miami, in Tampa, Jacksonville, and several other local governments.
To me, the biggest problem we have in Florida is our K-12 school system. Our public schools are a "unitary" system, which means that each county is a seperate school district. So we get one of two options -- 1) we have a school system like Miami-Dade (4th largest in the US) which is too large, too bureaucratic, and too corrupt to do anything but teach to the lowest common denominator, or 2) we have districts which are too small, and don't have the tax base to provide good education. Also, unlike many places, our School Boards are completely stand-alone governmental bodies, with their own tax source and complete autonomy. We do have some excellent school districts, and they tend to be in suburban counties which have good tax bases but are not too large and stratified. If I could change one thing in Florida government at any level, it would be the unitary school system.
We have an excellent community college system, and a great state university system, as well as tremendous scholarship funding through several sources...plus one of the best pre-paid college programs in the country.
We also have one of the best state parks systems in the U.S. Floridians tend to be quite environmentally-conscious, and we put our money where our mouths are. We are very aggressive in buying up environmentally-sensitive lands. We've spent almost $4 Billion of state money so far on Everglades restoration...just as one example.
Florida is a great state. We have our issues, like every state and locality does, but I wouldn't want to live anywhere else.
Oh well, at least it wont be such a long drive to the GA/FLA game each year. 
