I am a 20 year old full time college student. My parents don't claim me on their taxes. I still live at home, I pay for my own food, gas, school supplies, etc. I however don't regularly pay any of the bills of the household. I made around $13,600 last year. I also don't pay any kind of rent to my parents. Should I answer yes to being responsible for more than half of my support? Or should I answer no because I live at home rent free and only pay for my own things?
You can answer yes for providing more than half of your own support. If you want to be very specific, you can fill out Worksheet for Determining Support https://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf
Sounds to me like you really need to check the support test. Your parents most likely can claim you and because they are eligible you won't be able to claim yourself. The IRS was clamping down on dependents claiming themselves, so make sure you can fill the support test out accurately and hold it as support for your filing. Here is a link to a support test worksheet:
https://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf