I do a couple of things at this time of year. First, bookmark the National Hurricane Center's home page, and put it on your web browser's bookmark bar where you can quickly get to it. Second, I double check my insurance policy--seriously, make sure you are paid up and you've updated any information with your insurance company: change of address, new equipment onboard, change of marina, change of operators, etc. After you need to make a claim is not the time to notify your insurance company of some change that may have altered your coverage.
Other great sources of tropical weather information abound on the Internet. One of my favorite's is Dr. Jeff Master's WunderBlog. Be sure to read the comments from weather nuts too. The blog is one of the best sources of detailed predictions/guesses on what might happen a few days down the road. Fun stuff to read, but I find the Hurricane Center's predictions remain the best.
Another fun site to check out when we do get a storm is the National Data Buoy Center, where you can click on your favorite buoy or light tower to get up-to-the-minute on-site wind readings and often wave heights. I have Buzzard's Bay Tower bookmarked for fast access, and I also check out Borden Light, which is closer to where I keep my boat.
And, finally, it's not too early to begin preparing for the possible arrival of a hurricane. Keep your eyes out for sales on new dock and anchor lines. That spare hurricane anchor found in a yard sale now will be a bargain if you need it in August! Maybe figure out how you are going to rig extra-heavy mooring painters or dock lines, and don't forget to arrange for heavy chafing gear to protect those lines. I like to store and keep all this stuff organized and handy so that I'm not having to rush out to stores to find things at the last minute, which might be too late.