Are we talking focus cities/hubs or legal bases?

For the former, there's a whole load of LCCs that fit the bill (and quite a few in the latter, where they've had to set up legal entities in order to serve a particular country). In Europe, As well as Ryanair and easyJet as above, there's Wizzair, Flybe, Norwegian. Then there's a whole load in Asia-Pac - AirAsia, Air Arabia, Jetstar, Scoot...

There's airlines that serve bases in multiple countries through their subsidiaries (e.g. BA through Sun-Air and Comair). There's KLM Asia, set up to be able to serve the ROC without unduly upsetting the PRC.