If I am still claimed by my parents on their tax return do I get to claim the Tuition Tax Credit?

If you are still claimed as a dependent on your parents return, then they are the ones who get to claim the education credits. You cannot claim the education credits when you are a dependent. 

The qualifications of the credits are below:

 Lifetime Learning Credit

• You can take this for an unlimited number of years
• Twenty percent of expenses up to $2,000
• Non-Refundable meaning this can reduce the amount of taxes you owe, but if your tax liability is less than the LLC, your tax will be reduced to $0 and the rest of the credit is lost. 
• Cannot be claimed as a dependent on any one else's return
• As a Married couple, your income must be below $160,000 for the full credit and below $180,000 for a partial credit

American Opportunity Tax Credit.

• Available for the first 4 years of college
• Max amount is $2,500 per student
• Partially refundable credit meaning if your tax liability is $0, 40% (up to $1,000) is refundable
• Be enrolled in a degree or credential seeking program
• Not have a felony drug conviction
• Be enrolled at least half time
• cannot be claimed as a dependent on anyone else's return.
• As a Married couple, your income must be below $160,000 for the full credit and below $180,000 for a partial credit

Q. If I am still claimed by my parents on their tax return do I get to claim the Tuition Tax Credit?

A. No.  The tuition credit goes with the student's dependency.

 "It makes a huge difference in my taxes". 

That's unusual and is most likely due to an entry error. College age students are seldom eligible for the credit.

That said, if this is a case where your parents aren't eligible for the credit (their income is too high), there is a way for you to claim the credit. 

While technically there is a provision that allows a student-dependent to claim a federal tuition credit, from a practical matter it seldom works out.  A full time student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports himself by working. She cannot be supporting herself on student loans & grants and 529 plans and parental support.  It is usually best if the parent claims that credit.  

If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit.  The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)