In the Western Pacific, they cycle through a list of names continuously and don't start over each year. I kind of think the US should do the same instead of using Greek letters. There doesn't seem to be a necessary reason to start over at "A" each year. (But I also don't think grids for highway numbering are necessary either, so maybe it's just me.)
The first letter tells you if it's one of the earlier hurricanes or one of the later hurricanes. For example, just hearing the name Bob will tell me that it was very early in hurricane season.
I'm in favor of SEWIGuy's proposal here for one reason. While rotating A-Z lists may be attractive, I think it leads to problems when it comes to retiring names. Just look at the letter I. Usually the most destructive storms in a usual year happen around the tenth storm or so, which just so happens to be I's position in the alphabet. Think of all the nasty I-storms that have happened over the years. Irene, Isabel, Irma, Ivan, and Ike are just some of the worst I-storms.
If most deadly storms happen to occur when the Atlantic is on its tenth named storm, then coincidentally there should be lots of retired I-storms. The thing is, is that in the English language, there aren't many I-names that are popular, most of them are old-fashioned or obscure. This results in odd names such as Isaias and Imelda being used for storms (Remember how this thread blew up about Isaias's difficulty to pronounce?). The fact that the Atlantic basin is competing with the Eastern basin for names doesn't help matters at all.
The climax of my argument is that we may run out of good I-names eventually, and we may need to install a different naming system. Who wants hurricane Icarus?