Deane, my experience has been that the least expensive times are the two weeks before Christmas, and the first couple of weeks in September. However, sometimes prices fool you, and cruises you wouldn't expect to be inexpensive, are just that.
My advice has always been to book early, and make sure your travel agent keeps tabs on what's happening to prices on your sailing. If the price of your cabin category goes down, the cruise line will almost always refund to you the difference, or upgrade your cabin category. But you have to watch it; if the price goes down, the cruise line won't call you or your travel agent to tell you about it.
Cruise lines encourage people to book as early as possible, and therefore refund or upgrade. It used to be that people would wait until the last minute to book, and this wreaked havoc on cruise lines' inventory control. So now they say that the best prices are for the earliest bookers, and if they have to drop prices at some point, you won't lose out. And of course, the earlier you book, the better the cabin selection.
The more expensive times to cruise are high-demand weeks, such as holiday times, spring break, and mid-June to late August. Also, itineraries that have short seasons, such as Alaska and Bermuda, can be pricier than all year 'round itineraries.