WhichBudget.com is a searchable destination-by-destination database of 116 budget airlines serving 874 airports in 124 countries. Warning: this site may get you so excited you can’t sit still.
Want to find a cheap flight from, say, Vancouver to Hawaii in November? WhichBudget points you to WestJet, where you can do the round trip for about $500 before taxes. (Checking Travelocity, similar non-stops on the major airlines were already sold out for my randomly-chosen dates, although you could beat the fare if you were willing to route through Chicago.)
How about, I dunno, Los Angeles to Timbuktu? This took a little poking around and a bit of past experience, but in ten minutes I found connections on Point Afrique between the Malian city of Mopti and Paris, which you can skate to from Los Angeles via Ireland’s Aer Lingus. (Once in Mopti, most folks take the slow boat up the river to Timbuktu.) Total airfare, with a little planning: roughly $1500, round trip, before taxes. To Timbuktu.
My guess is you’re more likely to go to Hawaii. But just saying.
PS: if you’re concerned about the safety record of airlines you may not be familiar with — or, y’know, the whole zipping along seven miles up at 600 mph in a tin box thing anyway — AirSafe.com has the lowdown on whose tin boxes tend to go up and down as intended.