I never thought to write a post about it, but I use similar criteria when looking for an apartment. It's easier to switch apartments than houses, but it's harder to modify an apartment. This means that many of the criteria for apartments are more specific. Here are some criteria I use that Yvain didn't mention:

• East-facing windows. The sun rising in the morning is great at waking me up and forcing me to keep a normal sleep schedule. Without it I tend to go on a 26-28 hour day.
• Noise level. If possible, try to talk to some tenants. Try to gauge their age and propensity to make noise. I love living in an apartment complex full of older people. It's so quiet.
• Top floor. I can't stand people stomping above me. High-rises usually have better sound insulation, making this less of an issue.
• At least a block or two away from major streets. Big streets have more horns honking and are popular routes for emergency vehicles.
• Fast internet access. Often, only one ISP is available in an apartment complex.

This list has slowly grown as I've moved to different places and been plagued by different annoyances. My current place fulfills most of the criteria, although it's a little too close to a major street. Firetruck sirens are louder than most emergency vehicles; enough that they break my concentration if I'm not wearing headphones. On the other hand, the Internet connection is particularly fast: symmetrical 100Mbit.