For an encyclopaedic coverage of the subject readers are advised to consult the book Non-Uniform Random Variate Generation by Luc Devroye. It covers every imaginable distribution and provides hundreds of algorithms.
The subject of random variate generation is also reviewed by Knuth, who describes algorithms for all the major distributions.
The Particle Data Group provides a short review of techniques for generating distributions of random numbers in the “Monte Carlo” section of its Annual Review of Particle Physics.
The Review of Particle Physics is available online in postscript and pdf format.
An overview of methods used to compute cumulative distribution functions can be found in Statistical Computing by W.J. Kennedy and J.E. Gentle. Another general reference is Elements of Statistical Computing by R.A. Thisted.
The cumulative distribution functions for the Gaussian distribution are based on the following papers,