Some people are fearful of fall hurricanes, but cruise ships can deal with those by altering their itinerary, although you may see different destinations than what you planned.
Some locations have short cruising seasons. For example, if you are going to Alaska or northern Europe, you will have to cruise between May and September. If you are going to Antarctica, November through February is the season.
Going to the tropics is a little easier. The temperature will not vary much with the seasons. What does vary is the rainfall. The dry season for most tropical locations like the Caribbean and Hawaii is in the summer, and the rainy season is in the winter. This does NOT mean it will rain all of the time. You just need to be prepared for more rain. Afternoon showers are more common. Of course, if you are coming from Canada or the northern U.S., some warm rainfall is not a problem if you have left piles of snow at home!
If you are going to the Mediterranean, summer is the high season, but some ships cruise there year-round.
