Did you know that neither you nor your parents determine if you are a dependent after you turn 18? The IRS does and they have a specific formula to decide and it depends on how much you and your parents spend on you. However there is a twist, all student loans but not scholarships, for this, count as income.
To calculate if you are a dependent there is a very easy worksheet on pg 20 of publication 501 from the IRS, http://www.irs.gov/pub/irs-pdf/p501.pdf, fill it out honestly and you will know if you are considered a dependent for your parents according to the IRS. Often students are not considered dependents because of working or student loans but parents continue to claim them.
Overall it may be financially better for the parents to claim the child then for the "child" to claim themselves because it may allow for more deductions at a higher percent for the parents than the "child". For example, when I was under 24, my mom was being taxed at the 25% tax bracket and I was being taxed at the 15%. I would pay less in taxes than her for the amount of the dependent which was about $3000. However, technically, the IRS does not give parents that choice, if some how they find out they will force the parents to not claim the dependent and allow the student to claim themselves. Keep in mind this will cause problems with your parents and you may not want to force the issue.