Echoing what Matt said, there's no specific cutoff for R^2 -- generally, the higher the R^2, the better, but you have to keep a few things in mind.
A high R^2 doesn't necessarily mean you have a good model -- the coefficient estimates and predictions could be biased, so you would have to check the residual plots.
On the other hand, a low R^2 doesn't necessarily mean that you have a bad model. By definition, R^2 measures the variation in Y that is explained by the linear regression model. You could still have a good model if it turns out that the relationship between the Y and X variables is best described as non-linear. You can still draw important conclusions from your model even if your R^2 is low.
Something I would focus on is the RMSE, which is a measure of the accuracy of your predictions (differences between estimates and actual values). If your R^2 increases but your RMSE also increases, I would use the model that leads to a lower RMSE.
Hope this helped!