This TravelCodex post, the last of a series, tells all about the two elite status levels on Southwest Airlines. They are called A-List and A-List Preferred.
In may not seem obvious that Southwest would have status levels, since all the seats are in one cabin and any passenger can take any un-occupied seat. The primary benefit of status is early boarding.
To me, the best “status” on Southwest is the Companion Pass. The blog post tells a bit about the Companion Pass, and has a link to a more thorough description of what it is and how to get it.