Yafaray (http://www.yafaray.org/) might be a good first choice to consider for general 3D rendering. It's reasonably fast and the results look great. It can be used within other software, e.g. the Blender 3D modeler. The license is LPGL.
If the server-side software happens to be written in Python, and the desired 3D scene is a visualization of scientific data, look into MayaVi2 http://mayavi.sourceforge.net/, or if not, go for a browse at http://www.vrplumber.com/py3d.py
Those who suggest the widely popular POV-Ray need to realize it's not a library or any kind of entity that offers an API. The server-side process would need to write a text scene file, execute a new process to run POV-Ray with the right options, and take the resulting image file. If that's easy to set up for a particular application, and if you've more expertise with POV-Ray than with other renderers, well go for it!