What qualities do you bring to this job?

To answer this question, you need to have looked at the job ad for clues.
If it says, "The applicant needs to have several years experience in a similar field".

You would answer, "I have worked in this industry for several years and have gained good experience".

If the ad says, "The successful candidate needs to have problem solving abilities and be able to work as a team member". Guess what your reply should be?

Thats right. "I have a very enquiring mind and I like challenges. I am at my best when I have to solve problems".
And.
"I can work quite happily on my own if the need arises, but I do prefer to work in a team environment".

See this is not rocket science. The mantra you should live by whether applying for a job or in fact in any facet of your life is,"Tell them what they want to hear".