White Castle was a good 3:00 AM treat back in the 70's when I was traveling in their range. More recent encounters have been less satisfying. They say they haven't changed but it sure seems that way to me. Still, got to give them credit for having been around since before movies had sound.
About ten years ago IIRC KFC had a kind of chicken version of the White Castle Slyder. The were like 35 cents each and I was fiercely addicted for a time.
The one true great rival to In'n'Out has gone unmentioned: The Original Tommy's. They call it that because of the vast number of imitators. One thing first time visitors to Los Angeles will notice is a zillion little burger joints whose names are some form of Tommy. Tomas', Tommi's, Tomy's, etc.
Accept no imitations. Only the places with the logos seen on this site are the real thing:
http://www.originaltommys.com/
Tommy's goes back to the 1940's. Until just a few years ago there were a mere four locations, one of them in a location that is no longer considered safe for human passage. sometime in the 90's some big money stepped in and financed a big expansion and they added some items to what is still a very simple menu. Up until then they didn't even have fries. It was all about the burgers with everything done in slabs. Slab o' meat (up to three before bribery became necessary), slab o' tomato (none for me, thanks), slab o' onion, slab o' lettuce, and slab o' chili is you don't say otherwise. Cheese if you want it. The result is Greatness.
For many years I refused to have mine with the chili on it. I had a basic suspicion of chili on a burger to start with and the first time an older friend with wheels took me to a Tommy's (Roscoe and Sepulveda, across from the brewery) there was a parked car nearby and the guy sitting in the front seat with the door open spilled chili down his arm. I knew because he was alerting the entire neighborhood, "It burns! It burns!" It was reamarkably like 'The Exorcist.'
That put me off the chili for several years. I eventually succumbed to temptation and tried it. I'd been horribly mistaken all that time. I wouldn't think of foregoing the chili now unless I was in formalwear on my to instead of from.