Looks are always important I think, so once we get past that I would say these are the things that are important to me in a case to me;
It should be quiet (so pre-applied sound deadening is great and damped hard drives, rubber washers between the drive and the cage work well enough)
It should have front-top mounted USB and E-sata ports, I find it annoying when the ports are half way down the front of the case or even at the bottom like the classic Lian Li's. Also, E-sata, E-sata ...damn it E-sata is great, all cases should have an E-sata port on the front.
It should have thumb-screws to hold the case sides on for easy and fast access. Ideally though a step further would be nice, have a single thumb screw or locking mechanism that can be released and the side comes off like a Mac Pro (lovely design that, but I can't help feel it's wasted on Mac users who typically don't have their machine open every 5 minutes
./ducks)
It should use 120mm fans and in an ATX tower design should have room for 2 intake and 2 extractors ideally, extra fan points are a bonus though. Also the hard drive cage should be placed so that at least one of the intake fans cools it.
In an ATX design the hard drive fixings should be on those removable trays and side mounted, so you can slide your disks in and out easily, ideally, in a perfect world they would also have the sata and power connectors on a pcb mounted behind the drive tray so you never need to mess about with cables, like a Mac Pro. In an ATX tower room for at least 6 disks is ideal.
The materials used in the construction of the case should be strong and durable and have a quality feel. This is subjective I know.
A removable motherboard tray is a very, very good thing, I don't know why more case manufacturers don't include them. Might only be practical in an ATX tower.
Again for ATX the Power-supply should be mounted at the rear and bottom of the case, keeps it out of the way yet easy to access etc, doesn't mess with the airflow either then.
Also, a reset switch is very handy, why do so many cases miss these ? ...always put a reset switch in, hiding it behind a door is fine, just include on.
The nearest any case I have used comes to being perfect for me in the Fractical Design R2m, which gets close ...but could be better still ..albeit would cost more then I think.
Quiet but with good/decent airflow and nice clean looks (nothing too complicated) are probably my top ones though, if these aren't right I will look elsewhere.
. Not being able to fit my GPU in because the 8th 3.5inch drive is taking up its space is also a pain. The ease of instillation factor is mostly because I will NEVER install something correctly first time round.
simple looks timeless almost