Assuming you’re using Blender Internal renderer: If you have the hair material set to Traceable and it’s a fairly dense system (lots of parents and children) chances are you’re running out of RAM, which crashes Blender. Try rendering with Strand Render enabled in the Particle System parameters. Strand Render overrides raytracing (Traceable), so it’s a pretty good test and easy to do.
If you must use Traceable, try rendering with the Render>Performance>Octree option at 256 or 512. This can be a little slower than the other choices but also tends to use less RAM in one gulp. I can also give some tips on how to do more manageable Traceable shadows for hair systems, if it turns out that’s your problem.