What's the most important skill to have in your chosen field?

Flexibility! If you can be flexible, you can adapt to various situations. Expect change in any position or career.

It's difficult to pinpoint the most important skill since each field can vary drastically in the required techniques and skills.  However, I think that you suggested a great skill that can take you far in almost every field and that is being a great problem solver.  Each career is likely going to consist of a decent amount of problem solving regardless of the field.  Problems can be large scale (how do we solve this macro-economic issue?) or small scale (how do we fix the printer?).  The problems can also be those of someone else (such as someone you are managing) or those of yourself (such as how you manage your own time).  I think that in most day-to-day jobs, we're presented with challenges to solve daily.  The key to solving these problems is a great attitude and perseverance to continue to solve problems despite how long the problems may persist or any roadblocks that cause setbacks. 

For me, there are two important skills to have. #1 Time Management and #2 Flexibility.

It's important to be able to organize your day based on the priorities and also knock things off of your list. Usually I have a lot of tasks on my plate and I have to not only juggle them, but do them at the best of my ability. Flexibility can also take you very far! As your day begins, you week is shifting. Being flexible to accommodate other tasks or even just to be agile in changes within your job. Expect change constantly. This will also help your career growth.