Sorry for jumping into that thread, but I always wondered what makes a case a good case.
The case is the main aesthetical part of your PC. Therefore looks are always a factor. I know you wanted to discard that fact, but quite frankly, you can't talk about cases without talking about looks. Its like talking about cars and saying 'Yeah but lets not talk about the body, color, or interior.'

That means specifically what makes a case have a good air flow?
As you know, heat rises. Cases that take advantage of this fact and keep good bottom-front intake to top-back outtake
usually have good thermal performance. A single 120mm intake and 120mm outtake are in any heat-heavy system not enough by my standards. And I admit my standards are a little high, however in the summer some people let their ambient room temps get above 70F and that has an effect on your PC temps due to the fans taking in the air in the room. Thus, I always like to imagine 'This build is going to be in a room that is 80F year round, how can I make sure its sufficiently cooled?' to keep the PC safe from the worst-case scenarios, be it in a hot room or in a very air-restricted cabinet in a desk.
I imagined that a 120mm opening in the front and one at the back should be enough if you have fans there. How important are openings/fans to the top/side? Does top need a fan too?
It depends what kind of hardware you're packing into it. I personally like side-fans over the GFX because most GFX cards generate the most heat in the system and a lot of them have shitty cooling. In terms of importance: front intake + back outtake > side intake > top outtake.
Does quality matter? Personally, I never had a case that broke and I'm sure I had shitty cases since I always bought the cheapest.
I doubt you put quality components into said machine. If you're building a Dell-type machine with a shitty mATX board, RAM with no heat spreaders, and integrated GFX, sure, go throw it in a Dell-tier shitcase with one fan.

Panels are the sides of the case, in most cases you take them off when working on the PC. Very few cases have actual doors that open without coming off/taking the whole side off. Thin panels are just that- Thin metal sheets that are of low quality and are very flimsy. They like to bend, warp, and just be crappy.
And lets not talk about looks and other features that serve no purpose (like doors, sliders and whatnot).
What about other features like USB headers? Audio jacks? ESata port? There's a lot more to a case than just the cooling:
Cable management, acoustics, connectors (as mentioned above), space for components, weight.
Basically tell me everything I need to judge for myself which cases are good and which are not. And please lets keep brands out of it. I just want to know features.
A good case for a gaming machine has at least 4 fans: Front intake, back outtake, side intake, top outtake. Some have two in any of these spots, some have two in all of these spots. Generally speaking, fans should be 120mm or 140mm. No one uses 92mm or 80mm anymore and any fan larger than 140mm that I've seen, moves far too slow in the name of keeping noise down. If I could get a 240mm fan that spins as fast as a 140mm, that'd be great, it'd move a lot more air, and be quieter because its larger. A larger fan can move more air than a smaller one at a lower speed, thus making it quieter.
The case should also have at least 2x USB 2.0, mic and headphone jacks, as well as an ESATA port for good measure.
Finally, it can't be an Antec Hundred series.

I know you said no brands, but hear me out:
Antex Hundred series cases are of questionable quality and horrid style. They're the epitome of MORE LEDS MAKES EVERYTHING WORK BETTER!, the mindless mentality that bigger is always better (NV did this and now they're in trouble.), and that as long as you strap enough LEDs onto something it magically becomes quality. Antec does have some nice cases in their Performance One line, I really want an Antec P193 to be honest. But anyone who owns a Hundred series case is a hipster, a computer ignorant who thinks because they managed to assemble a list of parts someone gave them that they can have the title of enthusiast, that they actually know what they're doing. And they really don't. The CoolerMaster 500 and 600 series cases cool better than the Antecs and usually cost less. They're also of a much higher quality and do not have the hipster curse on them.
This is why I do not recommend Antec cases.