Southwest is not really the equivalent of Ryan. Spirit airlines has plenty of $22.22 flights (for two's-day, I guess), glancing at their page today. This includes e.g. Chicago to Tampa, Texas to NJ, and other flights longer than most European flights.
They look very much in the style of Ryanair with the garish website. $22 for three hours (Boston-Miami) is priced between the two Ryanair flights, so I expect the "service" is similar.
I'm sure the average distance of a flight within Europe is lower than in the USA, since the USA is a bit empty in the middle and Europe has more water in the way, but routes like Scandinavia to the Mediterranean (Stockholm to Zagreb is 3½ hours and $14), or Britain to eastern Europe (London - Cluj, 3 hours $13) aren't far off, and the budget airlines also have flights to tourist destinations in Egypt, Israel, Jordan etc, which are as long as a US coast-to-coast flight.
The cheapest flight I can see on SouthWest.com is $60, for a 1 hour journey from Atlanta to South Carolina.
The cheapest flight with Ryanair from Copenhagen is $9, though it doesn't include checked luggage. It's also an hour.
An even cheaper one is Kraków to Eindhoven, 2 hours, $6. There are fewer dates for this price though.