Formica you can either use a skill saw or jig saw to cut the overhang. Tape the line you are cutting in order to make a clean cut. Stay off the line 1/16th and take a belt sander to smooth the edge. I would suggest gluing another laminate edge on the cut side in order to have something to adhere the product.It may get hard to cut if it butts against the wall and may require removing the jigsaw base or using a sawzall
Solid Surface - (Corian) Carbide tip blade skill saw. Router with a straight bit in order to clean up the edge. The only problem is that you would need to take the existing cut-off material and glue it back on the exposed edge. You would have to purchase Corian glue somewhere. Please note that Corian can be refinished to look new again.
Granite - Diamond cutting blade....leave this to the experts and call a granite company. They would probably remove that section of counter and take it back to their shop to cut and clean the edge. Or take it outside in order not to dust out the house.