"Good rider" is so subjective it's hard to define. But MY definition of "good rider" is a person who, first of all, understands that every horse is different. I've seen lots of people get on a different horse and try to do everything the same as on their horse. Doesn't really work that way. Understanding that each horse needs to be ridden an individual way is key.
I am by no means some uber-talented rider. It's been a few months since I've sat on anything but my own horse. But the last time I rode a few different ones, I made it a point to take my time and figure out what worked for them.
I also think a good rider should be able to show his/her skill through the horse they are riding. If they can make a horse move better or softer or rounder or whatever the goal is, they have some talent.
Sticking to the tack makes a good rider, but that doesn't mean you have to stick to everything. Shit happens, and not everyone CAN sit out the back-cracking, bone-jarring, hip-twisting, nose in the dirt buck. I sure can't!
"Good rider" is also discipline specific. I know some basic dressage stuff, but I'm not a dressage rider. I've never taken a dressage lesson. I'm not good at that. Same with a dressage rider being good, or not good, at hunters or jumpers. Maybe they can hang on tight over a jump, but not necessarily find 8 distances and ride the course well.
A good rider doesn't blame the horse. Really, it's never the horse's fault.
And finally, a good rider knows there's always more to learn and isn't afraid to ask for help or a second opinion.
A good rider has the ability to read the horse. They will know what thoughts are going through the horses head, if the horse is having a good day or bad day before they even get on. They will know when the horse is overloaded mentally or is ready for a new challenge. They will know when to quit or to move on. They will know how to help a horse to learn, not just expect them to learn. They will know how to communicate with the horse.
I was speaking to a young girl last night with a green horse. She struggles with some basics, but does a nice job. I told her the key to riding is fixing the problem before it happens. It's a feel that one has, coupled with timing and subtle control of aids. If you watch a beginner, something goes wrong, then is fixed. If you watch an advanced (or good rider) it never goes wrong because it was anticipated and subtley fixed.
And I think there are degrees. I feel like a lot depends on your company. The mediocre grand prix rider is a good rider in the company 2' hunter riders. A 2' hunter rider might be a good rider at a barn specializing in WT trail rides.
To me, a "good rider" is somebody who:
1) Is a perpetual student of the theory of "horsemanship", and
2) Has good riding form, and
3) Can get the horse to perform to an acceptable standard, and
4) Can stay on the horse while that's happening (or not), and
5) Can manange to not be an excessive burden to the horse while doing so.
Need all five to pass go.
I agree with all 5 but would add a 6th and 7th criteria....
~can get on a horse while in the tack of any discipline even if it is not their own (dressage, h/j, western, saddleseat etc...) and make said horse go around nicely
~Is competent and confident both in and out of the ring