Every person hired works on a team so teamwork interview questions are logical and expected. Candidates often answer teamwork interview questions with "willing to work long hours" or "willing to help a person on my team" answers -- and fail.
Instead of answering with what you are willing to do for the team, answer with how you make the team better.
You deliver quality work so your team can count on you
What's the worst type of team member? One you have to do the work for. All. The. Time.
They never deliver their work when they say they will and when they do deliver work it isn't up to the quality standards the rest of the team has for their work. Consequently, every team member has to make up for someone as if they weren't even there.
So your very first answer to this question is to note that your team will rely on you because you deliver quality work on time. You can't just say it; you have to show it. Reliability on a team is an underrated quality, but one a manager completely understands.
You provide specialized job skills to the team
The strength of a team is that each person not only does his or her part, but also has a unique ability they share with the team that makes the overall team better. Even if you are interviewing for a position where every person on the team does one function, individual members will be stronger in some areas than others. This strength, or specialization within a team, helps the team do better at accomplishing goals.
Before heading into the interview, you need to compare your job skills to the job description. Then, you take your greatest job skill strength and use it to show how you can support the team using that job skill.
You confront without being confrontational
Clarity of thinking on the job is a lost art. Employees are afraid to question their manager (often with good reason...) and are afraid of confrontation on the team.
Yet confrontation is normal in any social situation and business is social. High performing teams are usually quite confrontational and display conflict because questioning their approach to a problem is how they come up with better solutions.
You want confrontation on a team. But you don't want to be confrontational when you are doing it. So what you need to do is show how you go about working with people, challenging their ideas, allowing others to challenge your ideas, all to get to a better approach to solving problems.
Let go of the lame teamwork answers
"Willing to help others" is a noble cause -- but not a reason for hiring someone. Or for rating them high on their performance review either. Teamwork is a job skill that needs developing, refining, and improving.
Showing how you deliver your work so your team can count on you, showing your unique contribution to a team, and helping the team confront their problems without being confrontational demonstrates teamwork.
Wouldn't you like someone like that on your team?