The main event every year for Gainesville is probably the Gator Growl. I hate to tell you - I'm not a sports fan, so I don't attend this. In fact, I avoid the city for this weekend, and either hole up in my house to avoid the crowding downtown, or take off somewhere else. However, I'm sure there are lots of information sources for this particular event for those that wish it.
Most of my events listed will be culturally oriented, as that is my preference. There are other things going on (especially sports) that I am ignoring :P
Other things that go on in Gainesville:
January/February: Hoggetown Medieval Fair
This is a small medieval festival held on the Alachua County fairgrounds. It has a living chess board performed by the Thieves Guild, birds of prey, animal rides (camels, elephants, etc.), morris dancers, and of course your normal crowd of vendors, performers, and other entertainments. One of the highlights (IMHO) is the band Empty Hats, formerly known as Double Indemnity. They are a very talented group that do Celtic folk music, and do it well. I've heard worse from nationally distributed CDs and such. And don't miss the Queen's Apples - sliced sour apples covered in homemade butter caramel, whipped cream and a cherry on top ;)
February: Westside Fine Arts at Tioga Town Centre
This debuted last year and was a great hit. Local artists and vendors got together in a newly built open air shopping center in Tioga, which is about 10 minutes from Gainesville, heading west. This is a new, upscale neighborhood with some very nice places around.
March: Santa Fe Spring Arts Show
This is put on by our local college, Santa Fe College, and has some wonderful artists from all over the country, as well as a section of community artists.
April: High Springs Pioneer Days
Head back to the old west and see some gunfighting, as well as shop among local vendors and information booths.
Summer: Not a lot of outdoor events happen during the summers in Florida, as it's simply too hot to deal with. However, downtown square holds summer concerts every Saturday evening for free, all are welcome.
October: Thornebrook Village Arts Festival
This is a high quality arts festival set up in the rambling open air mall of Thornebrook Village.
October: Butterfly Festival
This is great fun for the kids - it is held at the Florida Natural History Museum on UF campus, and during the days butterflies are set free every couple of hours. There are concerts, vendors, and activities for all.
November: Gainesville Fine Arts Festival
This art show was rated 23 in the country this year, though it's been in the top 200 for many years now. It takes over several streets along the downtown area, and has many fine artists from all over.
December: O'Connell Center Holiday Craft festival
This is a wonderful place to come for holiday shopping - local crafters gather at the O'dome, on UF campus, to sell their wares on Thanksgiving weekend.