There are many apps to watch free TV online but before I answer your question, have you considered HULU and Netflix? It truly can't be denied that these apps are amazing and for as little as $8.00 a month you can get unlimited content played into your tablet or cell phone.
Additionally, should you decide not to pursue Netlix or its alternative, you can always download the application you choose to be the best according to your taste, however, here are our suggestions:
IMBb Movies and TV
Google Play Movies
SPB TV and TVgo Plus Live TV