EasyJet
Going to Europe and want to make a few stops? EasyJet is going to be your best friend. I got a round trip fare from Copenhagen to London for $30 per person! EasyJet is exclusively in Europe with a few routes to Africa and the Middle East. This is a great airline to look into if you are going on a trip to Europe and would like to make a few stops. The connections will be considerably less than if you booked them through an American airline. Keep in mind that there is no drink service on these flights and they do charge for bags. Visit their website to sign up for their newsletter to get notifications on deals.
WowAir
Famed for their $99 one way tickets from DC to Iceland, Wow Air is an up and coming budget airline. Although Wow Air doesn't fly out of many US cities, you can find some great deals on flights from major US airports to popular European cities like Amsterdam, Barcelona, and Copenhagen. Once you find a great deal through them, find your own flight from your local airport to that major US airport that your Wow Air flight is departing from. I have noticed that Wow Air fares don't always show up on the popular discount flight search engines so you may need to look directly at their website. Be aware that each bag costs you each way on your flight so pack light to save even more!
Spirit Airlines
Spirit Airlines is expanding by the day it seems. With their "$9 Fare Club" you can get deep discounts on fares and bags for an enrollment fee of $60. If you plan on taking more than 1 flight per year with Spirit, you may want to consider joining. They also have a credit card that earns points faster and with less obligations and fees than many other airlines. This company is growing quickly and is keeping their points system very simple. They have flights to the Carribean, Central American, and the US, but none to Europe yet. I would recommend this airline if you live in one of the cities they fly directly from, especially for South American and Carribean travel. Visit their website to sign up for their newsletter, they have sales all the time.
Southwest Airlines
Southwest, the non-stop route king! In North America at least. This airline almost always has the cheapest fares for national flights within the US. They also have a few flights to Mexico and the Caribbean. The largest perk of flying Southwest is their baggage policy - first and second checked bags are free! They are also flexible with changes and wave changes fees pretty frequently which is good for those last minute issues. I would recommend checking their fares for travel within the US and the Caribbean.