1) Good airflow. This is probably the most important because, without good airflow, your computer might overheat and shut down. You'll want at least 2 fans, one in the front, and one in the back. Most rear fans are 120mm; some cases have a 120mm in the front, as well. Some cases have a fan duct on the side or on top.
2) Easy to work in. This ties along with the case being big enough to accomodate the hardware you're going to use. It will be hard to work in a case that's too small; you'll have wires everywhere, and everything will be very close together. Shoot for a mid-tower case with a toolless design.
3) Aesthetics. There are many different styles of cases; pick whichever you like; just make sure that it's a good brand.
4) Quality. No-name brand cases may have sharp edges which are dangerous for you and the wires inside. They may also be built out of thin metal which has a chance of bending if the case is moved a lot. Generally, you don't want to get the cheapest case you see, however there are some good cheap cases. Just read reviews online.
5) Weight. If you're going to move the case a lot, then you'll want to get a lightweight case. If it's just going to sit under your desk, then weight doesn't matter. Don't compromise quality for light weight; a case built out of thin steel will most likely not be durable. Aluminum is a good material for cases; strong and lightweight.
6) Brand. Lian-Li is widely considered to be the best manufacturer of cases, but there are many other good brands, including Antec, Thermaltake, Cooler Master, Silverstone, and others. Like I said before, don't go for the cheapest case you find, but read reviews online, as there are some affordable gems.
7) Price. Don't put $500 worth of components in a $250 case. $50-100 will buy you a nice case; only spend more if money is no object, of if you really love the case.