Transition to Agile. Which role is the most important?

Ranked by Importance:
1) Executive Sponsorship: If leadership doesn't drive it, it won't happen.
2) Agile Coach/Consultant: Someone with real experience to help the team transition. Getting a certification is not enough and is probably the most dangerous thing to have.
3) Product Owners: A Dedicated/Allocated Business Rep who understands and embraces this role will help the team deliver the right product.

Having done several Agile transformations the Executive sponsorship relevant to the scale of implementation is critical. A good rule of thumb is to get buy-in from at least 2 levels above the group you're converting. If you're converting all of IT then the CIO and CEO better have buy-in (if not the entire board) or else you're going to have real obstacles when it comes to HR.
The second most important role is a good Agile Coach or Consultant - and please don't use one of the "big boys" like PWC, Deloitte, Accenture, etc... as they tend to have LESS experience and are more rigid than more specialized companies and consultants. The Agile Coach will help you navigate obstacles and foresee challenges that an average CSM will not. When it comes to transformation, this ability to navigate and anticipate is critical to larger scale success.
The last more important role(s) are allocated Product Owners. Since this role sits with the business, this is usually the hardest to get because it needs to be a SME within the business which usually means this person was great at what they did, but now they have to transition OUT of that former role and into this one. Most organizations don't let them transition out, they just add more responsibility to this person. This is a huge mistake and the second leading cause behind transformation failure (behind no executive ownership).

We have considered the Agile Coach (an external one) because we knew internally we didn t have experienced Scrum Masters. The first try was a failure (because they had a start up approach) but the second time we managed to identify a coach who comes from development area in and worked in Agile/Scrum environment in large companies. The difference is visible.

Stelian,

I agree with your point on number 2, it is very hard to find a good Agile Coach. In my own personal experience I was mainly self taught in Agile until I was lucky enough to work with one of the good ones during my brief tenure in state government. She was, unlike many other "coaches", very encouraging of my practices and nuance in Agile while also willing to help point out where methods or practice could be improved. For us, it was all about perspective and practicality, not about adhering to strict rituals and ceremonies.

The biggest weakness in most coaches today are their unwillingness to tweak their recommendations to the needs and capability of the business. Too often they are rigid (an un-agile trait) and they keep trying to make round pegs fit square holes. All the more reason to vet and ensure you're getting a good coach.