This applet computes the complex roots of a large number of randomly generated polynomials and plots them in the complex plane.
By default, the coefficients on the random polynomials are independent Gaussian random variables with mean zero and variance one. Other distributions can be selected from the pull-down menu.
The theoretical density, as derived in this paper, is also shown for comparison.
By default, only 100 random polynomials are generated. Changing the value to a larger setting, say a few thousand, makes the computation take longer but the empirical distribution begins to look very much like the theoretical density.
Here's a screenshot showing the result using 5000 random polynomials...