You may not realize it, but eliminating this tremendous noise from your daily life is cheap and simple to do. The first thing you need to understand however is that it's not the pump that's making that noise. While your pump does make its own noises, the thud is actually coming from the check valve.
A check valve allows water to flow in only one direction, preventing back-flow of sewage or ground water that's being pumped out of your home. When the sump pump kicks in and flushes the ground water out of your basement, the water presses the check valve open as it flows through. When the pump shuts off, the sudden reversal of the water in that discharge pipe causes the check valve to close, creating the loud "thud" that you hear.
Some check valves, called silent check valves are designed differently to make them quieter. They cost approximately twenty-five dollars, and installing it is relatively simple. Hopefully your line has a shutoff valve above the check valve. It may look something like the red one in the picture. Turn the shutoff valve so you don't soak yourself in dirty water. Then remove the current check valve.
Once you have the noisy check valve removed, you can replace it with your new silent check valve. If your new valve is larger, you may have to cut the PVC piping to fit the new valve. Just make sure you don't cut too much off - measure before you cut.
Now that you've replaced your check valve, reopen your shutoff valve and away you go. Now you don't have to worry about that loud and crazy noise anymore.
You could also mount your check valve at a 45-degree angle. This will help to reduce the sudden reverse pressure and noise produced when the check valve closes. Also, make sure your discharge pipe isn't coming into contact with any part of your home's structure. If it is, apply some type of foam or sound dampening material around that spot to reduce vibration and noise.