When is it ok to remove the intercept in a linear regression model?

I am running linear regression models and wondering what the conditions are for removing the intercept term. In comparing results from two different regressions where one has the intercept and the other does not, I notice that the $R^2$ of the function without the intercept is much higher. Are there certain conditions or assumptions I should be following to make sure the removal of the intercept term is valid?