The Potential New Job
"What Do You Know About Our Company?" or "Why Do You Want to Work for Our Company?"
This is why you need to do research about the company before going into your interview. Interviewers ask this question to see if you did do research, which shows that you have a real interest in the job. Successful job interview responses to the question would be to explain what you know the company does, and mention a recent accomplishment or new development the company is working on. If you were asked why you wanted to work for the particular company, you can comment on the company's goals and outlook and how these relate to your personal goals.
"Why Should We Hire You?"
This will probably be a similar question to others you have been asked. Here, the interviewer is looking to see confidence from you, as well as how your skills suit the company. Try not to list general skills, and instead choose the three strongest skills that would allow you to succeed in this position. Re-state how you will be able to utilize these skills to contribute to the company.
"Do You Have Any Questions for Me?"
This question is similar to the one about your knowledge of the company in what the interviewer is looking for--professionalism and your interest level. It is always a good idea to come with a few questions prepared. Things you might ask about are any questions about the position in particular, such as whom you report to, questions about what it is like to work for that company, or follow-up questions, such as when they expect to make a decision.