This is very American-centric, although I suppose you have many non-US viewers…
In Europe as well as Ryanair mentioned above (in my opinion and experience, a very nasty company) there is Easyjet which has real fares ( I use them often) from about 5 euros (plus airport taxes) from, say, London to other European capitals. They tend to use smaller airports well outside the capitals, but still, it's cheap. You more or less have to book online, best is way ahead or be very flexible. Major carriers NEVER discount here, though of course they have cheap fares if you book ahead.
How To Find Cheap Airfare