It depends on the discipline. See the attached link for more information on the subject.

http://condor.depaul.edu/sjost/it223/documents/correlation.htm

Besides the discipline and the table provided by Edgar, it depends on the problem itself and the expectation of the community. In addition, while showing a correlation/association between two or more parameters, less R-Squared values might be acceptable compared to a case for which prediction purposes are considered. Overall, no distinct value could be presented to be acceptable for this statistical parameter. Finally, other goodness of fit indicators are of great importance and must be checked together with the R-Squared.

If your number of cases is more than about 10, then yes.  But it is important to use the logged values of $ because otherwise the relationship (r or R^2) will be controlled by 1 or 2 cases (you will see a wedge increasing some low to high values and violate tests of significance without using logs.

In general, your R-sqr is already reached beyond the threshold if we consider by discipline. Another important point has been clarified by Masoud, that it depends on the problem that you're going to address. You should look into other goodness of fit for your model, either all those are parallelly significant or not. In addition, I think we don't much concern about low R-sqr (even < 0.30, but > 0.10) in panel data regression. If you have panel data set, your R-sqr value is already strong. 

If  R square value is near to one at x% confidence interval and then it indicates that the regression model of the testing data is satisfactory. 

In other words R square is greater than 1-x% for the model,  which indicates that the regression model of the testing data is satisfactory

In statistics, the value or R^2 and its meaning are not restricted by the problem.  The significance is determined by standard tests of r that depend on the number of samples. The correctness of the tests of significance depends on not violating assumptions of linearity and normality of errors about the regression line.  The acceptable level of significance could depend on the problem.

Dear Respected colleague,

In order to assess the overall regression model fit in supporting the research hypotheses. This is done by, firstly, examining the adjusted R squared (R2) to see the percentage of total variance of the dependent variables explained by the regression model. Whereas R2 tell us how much variation in the dependent variable is accounted for by the regression model, the adjusted value tells us how much variance in the dependent variable would be accounted for if the model had been derived from the population from which the sample was taken. Specifically, it reflects the goodness of fit of the model to the population taking into account the sample size and the number of predictors used. Researchers suggests that this value must be equal to or greater than 0.19.

I hope this answer your question,

Best Wishes,

i