Dallas is Cowboys, Cowboys, Cowboys. The only thing I've ever seen like it when it comes to rabid zealotry from the natives is Texas Longhorn football in Austin. Austin is still a hippie dippie town in some ways, but Longhorns football is as huge there as the Cowboys are in DFW.
The Rangers are the second most important franchise locally. They have a solid and loyal core in their fanbase that has stuck with them throughout their history, which is mostly littered with failure. They draw two million even when they suck, which is usually the case. If the Rangers ever actually threatened to do some serious damage in the playoffs, it would be a big, big deal and the bandwagon would fill up quick.
The Mavs and Stars I think only really thrive and draw when they're good. The Mavs are a distant third in importance to the Rangers and Cowboys, but they've outperformed them in meeting fan expectations for the past 10 years.