More details would help a lot but going on the details you provided. I would guess possibly a defective strut or strut mount. A defective spring or one of its components. A defective shock and or possibly a bad ball joint. I would try pushing up and down on each corner of the car and see if you hear the sound then try to pin point where the sound is coming from and go from there. If you still don't know see a pro. , EzForJesus
This may be too simple of an answer so i apologise if it is too simple but your 96 Intrepid is equipped with anti-lock brakes. When your brakes lock up by pressing the pedale reall hard the car automatically will pump them at a super fast pace helping to slow the car better. Your car also might come with "Traction Control" Basically what this does is if the wheels are spinning it again will use the anti lock feature to try to regain traction so you may feel the same thumping on ice or real wet roads.
Check the lug nuts immediately. Check tha clip that holds the brake pad on. I had a loose pad that made more of a tick sound that went away when I pressed on the brakes
I would check brakes,shocks,and powersteering pump. I would check brakes,shocks,and powersteering pump.
Take it to the garage and have them check for a cracked rotor or a loose caliper.
get the person out pf your trunk...lol
brakes may need bled but more than likely vacuum booster is bad
Is it accompanied by a shuddering or vibration? You could likely have bad brake rotors.
you might have a vacuum leak in your intake manifold
Could be universal joint is finished. A bad flex disk
Maybe broken motor or transmission mount
i don't know if this helps but i just had my car repaired tonight and when i picked it up this was a new problem that wasn't there before. i took it back and they said the thumping was caused by a rotor??? that they forgot to tighten? i am not sure i have the name right!
The caliper may be hanging and causing the humming sound. I cant type the sound out but it mine made a humming noise as the wheels turned. If I pressed the brakes hard and quickly let go it would stop. I just replaced rotors and brake pads and it is back to normal now.
I would advise bringing your car to a mechanic as quickly as possible. Your brakes could fail. This puts you at a high risk for injury or even death.