I am trying to find the spin tool in Blender version 2.68. It's not on the left panel. Should I check something in the preferences?
Here is a screenshot:
The spin tool does not work with curves, it's specifically made for meshes. There aren't really any alternatives other than rotating around the 3D cursor.
To rotate around the 3D cursor:
Extrude e and rotate the curve.
Tweak the handles so it's curved:
If you don't care if the object is a curve you could convert it to a mesh (Altc) and work with it from there.
The spin tool is for mesh objects.
For curves you can get the same result using two curves, one for the outline and one for the 'spinning'. The outline curve is set as the bevel object to the spinning curve. For a 360 degree spin a BezierCircle is a good starting point.