Travelling off-season might not be an option for all of us (teachers, families with school aged-children, etc.), but for everyone else there are great advantages to visiting a place outside peak times.
Time of the year. Now even I wouldn’t go to the Caribbean during hurricane season, but I know many people who have taken the risk and it paid off. Often they get amazing weather and always they get big discounts. If you want to play it a bit safer, April/May or early December in the Caribbean generally mean good prices combined with nice weather. My favourite time to visit Europe is September/October. The weather is still warm but not so hot that you can’t tour around, plus the line ups at attractions are so much shorter and flight prices can be significantly cheaper than summer months. In North America, consider staying at country resorts, cottages or spas in the spring, fall or winter. There are often plenty of indoor activities, cozy fireplaces, and it won’t be as crowded so you can really relax.
Time of the week. Weekends usually mean the highest prices both for flying and accommodations. I sometimes book a weekend getaway on a Sunday night, rather than on a Friday or Saturday, for big hotel savings. Of course it does mean you will have to take a day off work. From my experience, flights prices tend to be cheapest when departing on Tues/Wed/Thurs and all inclusive packages are also usually cheaper if you don’t fly out on the weekend. Early morning departures can save you big bucks as well, if you can stand getting up that early!