This video describes some good examples of various router jigs (or templates) and their application. Used in conjunction with a flush trim router bit or router collar, a good template will allow you to cut precise, complex shapes with relative ease.
The basic idea is to make the mistakes and adjustments on an inexpensive jig prior to making a cut in an expensive piece of hardwood or veneer plywood. If the template doesn't look exactly how you want it then it is easily fixed or adjusted prior to making the actual cut.
The narrator makes an excellent point that router templates need to be very smooth and true. Bearing guides and collars follow the template exactly, which means that any imperfections in the router template will also show up in the piece you're cutting.
He also mentions the use of hardboard for use as a template material. I agree that hardboard makes excellent router templates, especially if the template is to be used over and over. The hardboard will stand up well to repeated use.
MDF also works very well for router jigs, but try to stay away from using plywood or particle board. Unless you're using plywood with a high quality core then the edge will have voids. This prevents the bearing from smoothly following your desired shape.
Particle board could be used in a pinch, but it's difficult to get the edge perfectly smooth as with hardboard or MDF. The particles themselves are often large enough to create small bumps in the edge. Also, particle board edges tend to chip and crumble with use and handling.
So stick with hardboard or MDF and be sure to sand the edges perfectly smooth and true. The resulting template will then allow you to cut a precise edge on whatever material your project calls for.