Triangle, by Jonathan Shewchuk of Carnegie-Mellon University, is a C language code which generates Delaunay triangulations, constrained Delaunay triangulations (forced to have certain edges), and quality conforming Delaunay triangulations (which avoid small angles by inserting extra points). It has been widely used for finite element analysis and other applications, and is fast and robust. Triangle would be the first thing I would try if I was looking for two-dimensional triangulation code. Although Triangle is available at http://www.cs.cmu.edu/~quake/triangle.html, it is copyrighted by the author and may not be sold or included in commercial products without a license. Also included is a package by Shewchuk for robust computation of geometric predicates using exact arithmetic.