thats your sway bar. it helps transfer weight from one side of the car to the other in turns.
you can remove it without too many ill effects (obviously heavy acceleration from a stop, such as in drag racing, and turning will be effected. You'll feel much more body roll during the turn.)
you can find a junk-yard replacement for a couple of bucks....
you can find a used OEM cobra one (1996-1998 cobra) for a budget-friendly upgrade...
you can find aftermarket versions to increase performance even further.