Do I have to pay taxes on my scholarship?

In 2015 I received a $7500 scholarship—$3500 went to tuition and fees, $1200 went to books and the rest ($2800) was mine to keep for personal expenses? Is any of the leftover amount taxable at all? Should I be worried?

Yes, the $2800 is considered taxable income (in general, money that does not go towards tuition+fees+books is taxable). You’ll need to include that income when considering if your total income (earned from other work and this) puts you above the filing thresshold.

See https://www.irs.gov/publications/p970/ch01.html

Why worry about free money? Even if you are paying taxes on it, it is still more than you had before. Also you may not make enough to actually pay tax. Just keep records of what is received and what is spent on what. Only qualified expenses are exempt, as mentioned above:

=tuition and required fees, books, supplies and equipment.

The rest is part of your income for tax purposes.