Since all companies and corporations are different and since there are different positions, the criteria will be variable. For example, if a school is looking for a teacher, then the school would be looking for the ability to teach. If the school is looking for an administrator, then the school might want organizational skills. If the school is looking for someone who will be around for a long time, then the school might care about collegiality. In fact, the school may want all of these characteristics.
If we change the setting a bit and move over to a finance firm, then the ability to teach would not be too important. Instead what they want would more likely be quantitative skills.
In short, criteria change.
With this said, a few characteristics seem always to stand out: intelligence and honesty.