Marion Fourcade sent me the link of this interesting site, the Government Indicators Database published by the Inter-American Development Bank:
It mainly aggregates standard datasets, with a fancy interface. But, it has some governance measures that I hadn’t seen before. And, it is certainly nice for quickly looking up data on a specific country.
NOTE: It does have longitudinal data on many variables, though it takes some clicking to find it.
World Society, Institutional Theory, and Globalization 
As always, these data ought to be used with caution. First, a lot of the important variables having to do with governance, rule of law etc… are based on opinion surveys of a small sample of business executives! Second, some variables are inconsistent with the description of the coding scheme. For instance, the descriptive notice for the ‘legal origins’ variable, which codes countries’ commercial/business law according to the principal source of their legal system, is erroneous. Given the way countries fare on this measure, it should be 1 English 2 socialist, 3 French, 4 German and 5 Scandinavian.
Yes, I agree 100%. Some of these sources are good, but others are really problematic for most kinds of research. But, also good to know that there are some coding errors in the data… Thanks for catching that.