1. Slackness and Fit: It's really annoying if your case doesn't fit your phone snugly. Some cases stick really tight, while others are a bit loose. My most recent purchase was slightly loose; not ideal unless you want debris getting inside. The looseness wasn't in the case itself, but near the charging port. This is the one feature you may be able to test before purchasing; ask the retailer if they have demo cases or will let you open a pack to see how it fits before you make a decision. Be sure to check the fit all around, but also at any seams or openings.
2. Degree of Protection: The main reason for getting a case is to protect your phone from the occasional spills and scratches that occur with normal usage. A material that's too thin won't do the job adequately, but too bulky and comfort/ergonomics suffer. Aim for the middle ground.
3. Sturdiness: Case materials available today vary considerably, ranging from sturdy to somewhat flimsy. I had one case that was made of a sturdy plastic that barely got scratched in months, while another that was transparent in the back got massively scratched in a week.
4. Charging Port Access: Unless you like the tedious process of removing a case every time you charge, it's paramount the case allows for easy access for charging. Fumbling around with your phone when you're tired isn't always a good idea and thus you want to make sure any case you purchase doesn't hamper access. Most cases will fit snugly around the charging port, but others will make it harder.
5. Headphone Access: All cases offer access to the headphone jack, but some of them allow only very thin jacks, like the one on the Apple headphones. Make sure there's enough room for the jacks of all of your headphones, even the higher-end ones. Usually, this isn't an issue, but my most recent case won't allow me to use an extension cord for my headphones.