Here's what I look for in a case. Large fan grill. I like cases using 120mm fans because it's less noisy and has large openings for the air to flow through, creating less noise while providing the same amount of cooling as a high RPM 80mm fan. Also look for a case with good air flow. Cheezy fans have a stylistic fan grill that absolutely chokes the air flow.
Next is the insides of the case. I don't necessarily look for removable mobo trays but I do want the case to be roomy enough that I can work in it without problems. Features like removable drive cages, drive rails, and lots of thumb screws are good too. Although if the case allows easy installation of the optical and hard drives I don't necessarily mind having to screw them in the old fashion way. And very importantly look for a case that won't require a whole box of bandaids after you're done installing.
Somewhat related to internal features is a bezel with integrated CD/DVD drive covers. I like cases that have an integrated cover. It's not that much more expensive to implement yet you don't see it sometimes even in pricier computer cases. It hides the optical drive and gives a uniform look rather than the checkered flag look some cases turn out to be after installing a couple of optical drives. I had this one computer that had a beige case, a silver dvd drive and a black dvd drive. Looked horribly mismatched. I also like integrated input plugs somewhere on the front. My case (Antec P160) has firewire, USB and audio plugs easily accessable in the front.
Last, but not least is style. The outside looks of the case should be the last area you look at. It should be pleasing to your eyes and your eyes only. I personally hate the flashy and garish cases but some people like them for instance. If you get a flashy case, just make sure one year down the line you will still like it and not come to hate it. Investing in a good case might be a better choice than getting a cheap one. You might be ecstatic with your computer case and use it for years to come while the cheapish case you buy now may irritate you in only a few months time.