Among American Opportunity Credit, Lifetime Learning Credit, and Tuition and Fees Deduction, which one is most beneficial for students, and why?

The American Opportunity Credit.  It's 100% of the first $2000 of tuition and 25% of the next $2000; $2500 maximum.  It's 40% refundable (you get up to $1000 even if you have no tax liability).

The Lifetime Learning Credit is 20% of tuition (max $2000) and nonrefundable.

The Tuition and Fees Deduction is only a reduction in taxable income. It's value depends on your tax rate, but for most people it's worth $480.

But be advised, there's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants.  It is usually best if the parent claims that credit. 

You cannot claim a credit, or deduction, if you are, or can be, claimed as a dependent by someone else.