I'm not certain as to what I need to file, tax-wise.

I have been in the United States for 2.5 years on an F-1 visa. No dependents or anything. I am therefore pretty sure I have to file the 1040NR (or 1040NR-EZ), as I don't think I can claim residency status for tax purposes.

Can anyone explain to me why my return using the 1040NR-EZ (done by hand) is $21 and when I enter the same values into the 1040 (done by TurboTax, which has no option for the NR forms), I am owed over $1400? Is the standard deduction for Americans really that good? Or am I doing something wrong somewhere?

On an F1 visa you are exempt for 5 years from counting days for the substantial presence test which would mean you are a non-resident alien for 5 calendar years. YOu need to file form 1040NR or 1040NR-EZ. You cannot claim the standard deduction as a non-resident alien unless you are a student from India, but you can itemize certain deductions.
The standard deduction reduces the taxable amount by $5700 (for single filers), so yes, residents save income taxes. On the other hand, you don't have to pay social security and medicare as a non-resident alien.

Thanks awfully. I guess it was just alarming to see the massive difference between what I'd pay as a resident and what I'm paying as a nonresident. Thank you!

You will file nonresident tax return and form 8843. You do not get standard deduction. Instead you get itemized deduction and deduction as per tax treaty. http://taxipay.blogspot.com/2008/03/us-tax-filing-requirements-for-non.html
What is your citizenship?

I am Canadian. I was under the impression that if we make more than $10,000 USD in one tax year that the treaty does not apply to us. Is that correct?

This is from IRS publication 901. Tax Treaties.
"A student, business trainee, or apprentice who is or was a Canadian resident immediately before visiting the United States, and is in the United States for the purpose of full-time education or full-time training, is exempt from U.S. income tax on amounts received from sources outside the United States for maintenance, education, or training.
Apprentices and business trainees are entitled to the benefit of this exemption for a maximum period of 1 year.
Also see Publication 597, Information on the United States–Canada Income Tax Treaty."