If it is a circle then a circle cutting is easy to make and use.
http://www.woodworkingtips.com/etips/etip102000sn.html
If it is not a circle you need to draw out the pattern on a piece of plywood. Cut the pattern using a bandsaw or jigsaw. Tape the pattern to the workpiece with double sided tape or clamps if you have the access. You can then either use the bit Kirk referred to or you can just use a straight bit in conjunction with a router template guide.
http://www.amazon.com/Porter-Cable-...ref=sr_1_1?ie=UTF8&s=hi&qid=1245374381&sr=8-1
If you use the straight bit/template guide combination you will need to allow for the thickness of the template guide and the difference between the ID of the guide and the diameter of the router bit.
You also mentioned that the groove you need to cut might be require two passes. I don't think moving the template will work. The geometry of moving a curve will not give you a groove with two parallel sides. You would need to cut a template for both sides of the groove and then run the router up one side of the template and down the other side.
Whichever method you use a plunge router would be easier, unless you are able to come in from the side of the workpiece.