Install blocking between the floor joists to make the floor more solid and less mobile. Measure the distance between two joists and cut a piece of wood that is the same dimensions as the joists to this length. If your joists are 2-8s on 16-inch centers, your blocking will be a piece of 2-by-8 that is 14 1/2 inches long.
Tap the blocking in between the floor joists until its top meets the sub-flooring at the top of the joists. Secure it between the joists by driving 3-inch-long screws through the joists and into the ends of the blocking.
Install a row of blocks, staggering their positions so you're able to drive screws into all of the ends.
Secure the sub-flooring and finish flooring to the joists in squeaky places using screws. Have someone walk around upstairs while you are in the basement. When he locates a squeaky spot, have him stand on that spot, then drill a pilot hole at a 45 degree angle through the floor joist, near the top. Drive a screw in so that it goes through the pilot hole and into the sub-flooring and finish flooring. This will immobilize the squeak.