Formative Assessment: To grade or not to grade?

I recently participated in our district's "Standards Implementation" workshop with the high school implementation teams.  The main focus of the day was formative assessment.

Our district presented their definition and some of the defining characteristics of formative assessment.  Below is what I took away from our district definition and characteristics.

Formative assessment is the assessment of learning that takes place while the student is developing understanding of desired learning.  Formative assessment is tied to the standard and should occur in your classes frequently in order to inform instruction, provide evidence of learning and give timely specific feedback to the students.  Formative assessment is done individually or in groups, and it should be safe with no negative consequences, not used as a behavioral consequence and should not be graded.  

One of the sticky points for teachers about formative assessment is the idea of not grading the work. Many teachers believe students will not do their best effort if there is not a grade attached to the assignment.  

So my questions:
Should formative assessment be graded?  
Should it only be used to inform instruction and provide feedback to students?  
Will students put forth their best effort for work not graded?  

Share your thoughts in the comments.