Best Time of Year to Visit -- As with Walt Disney World, there's really no off season for Universal, but the week after Labor Day until mid-December (excluding Thanksgiving week) and January to mid-May (excluding spring break) are known for smaller crowds, cooler weather, and less humid air. And you won't have to worry about the daily thunderstorms that often plague Orlando during the warmer months. The summer months, when the masses throng to the parks, are the worst time for crowds and feature hot, sticky, humid days.
The Best Days to Visit -- Go near the end of the week, on a Thursday or Friday. The pace is somewhat fast Monday through Wednesday, with the heaviest crowds on weekends and during summers and holidays. If you do end up visiting during peak seasons or on holidays (when the parks are open late), consider waiting until late afternoon and staying until closing time -- after the dinner hour the parks are generally much less crowded.
Note: Universal Studios Florida is probably the best of all the major theme parks to visit when the weather is bleak because the majority of its rides and attractions are indoors (there's still a ton of walking outdoors, but at least you don't have to worry about many of the attractions closing because of lightning or heavy rain). A shower or two is almost inevitable in Central Florida on a summer afternoon, but if the forecast for the day calls for a sustained downpour, then USF is a great bet.