For Europe at least, this site on Seasonality in Tourism Demand for Europe is going to be a great start - it has graphs galore, detailing which countries get how many tourists, and why, and when. It's a really good read.
Now, to do your own research is probably the best way to find out low season for any particular destination. You'll want to investigate a few factors..
Climate - researching what the expected climate is in the destination you choose is very important. Rainy seasons, seasons of irregular weather, extreme heat or cold can all ruin a holiday. This really is one of the most serious considerations when choosing an off peak holiday.
Attractions - many places you may wish to visit, the attractions are seasonal. Hawaii is warmer in summer. Northern lights are barely visible in summer - best in winter. Snowboarding is best in winter - you need snow, for example.
Air fares - many airlines tweak their fares for seasonal demand. You can use kayak.com to check fares ahead of time, and set alerts for when deals appear.
Hotels - similar to airfares, you can set alerts on some booking sites (booking.com, and check ahead to see when deals or discounts appear. Planning is essential, sometimes airfares and hotel deals aren't available for long, so if you know your dates and budget, you can take advantage of the deals when you see them.