This cartoon (by www.claybennett.com) illustrates the effect of money, or better of rich people, on government. If we limit ourselves to the best cases, i.e. mature western democracies, then I think it is safe to say that the judiciary is the least affected by this problem. You cannot, or with great difficulty, pervert the course of criminal justice by using your money. You can’t bribe judges or juries. What you can do is afford a good lawyer, and hence obtain better justice than poor people.

The effect of money on the legislative branch, however, is more important. The problems of party funding are well known, and some democracies try to limit it because it creates some kind of moral debt towards the donors. Hence these donors have too much influence in a system dedicated to equal influence. The same can be said of the executive.

But of course apart from funding, more wealth can mean better education, more information etc. and hence better political participation.