Any weekend in April or May is a good time to begin clearing away rotting limbs and trimming trees and shrubs in preparation for hurricane season. This is critical in helping to prevent damage to your home and improve the ability of your power company to restore power in a timely manner after storms. It is important that people keep the overhang of trees away from their home and power lines. If tree limbs are near power lines, call your power company. Often they will trim those trees for you or they may suggest a licensed tree-trimming contractor for you to call. Do be aware that in some cities you might need permits for tree trimming.
This would also be a good time to take a look around your yard and make a note of items that will need to be secured or brought inside before a storm. The PalmBeachPost.com has a wonderful article on How to Prepare Your Yard Before the Storm. This would be a good article to print and save since they offer tree-trimming tips, a list of trees that faired the best in the 2004 hurricanes and other pre-storm preparations for your yard.