Correct ?

No, it is not fluent.
You want to be responsible is not a good sentence.
Instead, you had better write I am responsible or I want to take the responsible of this xxx( a situation eg. Accident, quarrel...)/ this job

2013-09-29 18:10:15 補充：
Or I want to take responsible for xxx( a situation/ thing)

2013-09-29 22:01:13 補充：
Yes

2013-09-29 22:02:15 補充：
But you had better write 'I would like to be more responsible'

Dear Wood,

I think both statements you mentioned are correct.

For Answerer 001, if you consider using "I want to take", then use "responsibility".

For Commenter 001, both statements are correct.

For Commenter 002, that would be a more detailed statement.

2013-09-29 19:25:40 補充：
Your sentence is also sensible, depending on situations.

Teacher said, "How come you are such an irresponsible student!"

Student said, "I want to be responsible, but I am too lazy, sorry..."

=^o^=

I want to be responsible for ...... .

I want to be more responsible.

I want to be a responsible person.