How would you react if one of your team member takes initiative of crucial task's decision without coordination with you?

As a Team Leader, we should be able to evaluate the issues professionally and thoroughly, first we should find out the reason, and if the initiation was necessary and could not wait, then it could be excused. But everyone should be given a second chance, unless the initiation made is harmful to business and breaches the employee contract severely, then immediate termination will require

I will tell him or her bad decision, but good job if you do it again you are out.

You can be a good leader but you have to be a good soldier first.

I will promote him or her if they follow plans.

If this has been done on an emergency where I wasn't available, I will be proud of him; especially if the said decision resolved the problem.

In private, I can ask more questions about the decision and give some advices if this have to occur in the future.

I may presume that it is with the implied authority of the immediate or higher controlling authority, represent the matter with him for a voluntary withdrawal from the task.  Anyway  I wont work with the team further, if he is within the team in order to avoid further personal conflicts.  

I agree wih all answers been added

It would be so dependent on the circumstances. If he/she had to make an "on the spot" decision and you were unavailable then I would applaud their initiative regardless of the outcome of that decision. The "whys" and the "wherefores" of the decision can be discussed in private later purely as a "lessons learnt" exercise. If one of my subordinates has deliberately "gone over my head" and chosen to make a decision which they KNOW is my responsibility, then they will have a lot to answer for, again regardless of the outcome of that decision. They know that they have overstepped the mark and should be prepared to accept the consequences.

I would appreciate his initiative and support him from whichever stage of the process that I learn of it. Gradually, I would drive the point home that it is important to work while keeping the relevant stakeholders in the loop. Nothing personal!

I will support him/her anyway to make that initiative successful but will let him/her realize that its better to take teams consent to involve them properly. 

According to situation.

He could manage and take immediate decision for a critical one, in this case you should thank him or her.

in normal situations he or she should follow the rules, or else you guide him or her verbally 3 times , then give a written warning, finally give a penalty.     

avoiding or ignoring is not acceptable. if successes, he/she will be appreciated. but not encouraged. 

mean time, i am trying to involve as responsiblity