When coming to a sudden stop there is a slight shaking and clunking feeling felt in the brake pedal. This only seems to happen in situations when I'm coming to an abrupt stop. I've also noticed it happens more frequently if I've driven over a puddle or a wet roadway. Is this something that I should fix immediately?
My car has 175000 miles.
My car has an automatic transmission.
This sounds like you are feeling the anti-lock brakes working as they should. Sometimes when the rotors get warped then your brakes can lock up earlier than normal and the ABS kicks in. You should have the brake system inspected by a qualified technician, like one from YourMechanic, to address any potential issues.