Great question.
I start out with three basic criteria before I get more detailed about my decision.
First, the industry. A company has to be well-positioned in the industry I want to work in. If I have a high interest in infrastructure, then I'll look for companies like Bechtel, Exxon, KBR, and others in the heavy industries. Or, if the company isn't a direct provider in the industry, I'll look for an investment bank or consulting firm with a presence there.
Second, function. I want to be sure that the positions available meet my skillset and are actually in-line with what I want to do. This should be pretty obvious.
Third, culture. If I'm not already familiar with some of the folks at the target company, I need to find out as much as I can about the work culture there and the overall "personality" of the environment. For example, if I'm the kind of person that enjoys working long hours, I probably won't do well in a culture where everyone leaves at 4pm every other day for happy hour.
Once those basic criteria are met, then I start looking at the other details. These include salary, bonus opportunities, career growth potential, location, etc.