Generating Random Orthogonal Matrices

If you sample elements from a uniform distribtution over $[-1,1]$ and apply the Gram Schmidt procedure, you can generate every possible orthogonal matrix (note that orthogonal matrices necessarily have elements within $[-1,1]$). However, I don't believe that it will generate all matrices with equal probability.

See this paper for further discussion, and a method that produces a uniformly random unitary matrix.