Can my boyfriend claim me as a dependent living with him for 2 years?

If you did not work during the year and he paid for over half of the expenses if keeping up the home then yes, he can claim you as a dependent on his tax return. He cannot use you as a qualifying dependent for Earned Income Tax Credit though. Also, if you do not have health insurance he could be penalized for you not having insurance if you are a dependent on his return.