Wow, a lot of ground covered here since I last checked this thread. Capsule response time!
In-N-Out: I've been here once, during a Christmas stay in California. It was crowded as hell, but I can understand why, as this was a thoroughly satisfying burger experience.
White Castle: REPRESENT. I've only had a handful of run-ins with White Castles in my life, but all were joy.
Sonic: I went to Sonic a few times in high school; they made a good burger, although not an extraordinary one. They were one of those "drive-in" places that basically did not allow you to order in person even if you came in, which made eating in very odd.
Chik-Fil-A: Why are there not more of these places? They seem to fill a very satisfying market niche, but I think I've eaten at one of these in my life.
On the subject of "obscure and possibly regional burger joints," many of my better recent hamburger experiences have been at one of these. The two that come immediately to mind are both solely Midwestern: Runza, run out of Nebraska and infamous for selling very nice (if very fast-foody) burgers along with their flagship pierogie-like sandwiches, and Culver's, a chain that appears to be entirely about high-quality burgers and delivers.
I was planning to end this post with a long rant about elitism and the great frustration to me caused by those who shun the common simply because it is common, and because a a disdain for the common is generally considered necessary to appreciate better qualities of things, but I sort of lost fervor. Suffice to say that I like hamburgers, refuse to yield my liking of hamburgers to an outside force, and will defend to my dying breath the idea that fast food is a perfectly justified topic of discussion for this forum.