If you really want a great mesh with some guaranteed properties, not just a Delaunay triangulation (which can still contain small angles), look into the work of Jonathan Shewchuk.

For example, for 2d mesh generation:

http://www.cs.cmu.edu/~quake/triangle.demo.html

He also solved the problem of degenerate cases (e.g. four vertices exactly on a circle) with adaptive precision floating point arithmetic.