Question: Some land-based fighter aircraft have a drogue-chute to help them slow down during landing.

* Do any current models of commercial aircraft have a similar
mechanism?
* Secondly, would such a mechanism help aircraft in making a better landing and reduce landing related incidents/ accidents?

Answer: 
It is called a [drogue parachute](https://en.wikipedia.org/wiki/Drogue_parachute) and I don't think that any of the present generation large commercial aircraft use them. 

That said, a number of older commercial aircraft have used them, a good example being the Sud Caravelle.

[![Caravelle drogue](https://i.stack.imgur.com/vQgzK.jpg)](https://i.stack.imgur.com/vQgzK.jpg)

Image from eu.airliners.net

There are some issues with using drogue chutes in a commercial airliner, which would limit their effectiveness.

* Most commercial airliners have thrust reversers already.
* For it to be effective, the parachute has to be quite huge. For example, the Handley Page Victor, which had MTOW in the range of A320, had a drogue chute 48' (or 14.6m) in diameter. The chute would occupy volume and increase weight.
* If drogue chutes are used, they have to be packed before every flight, which will increase turnaround times. Another option is to replace them at the end of every deployment, which would increase costs.
* Deployment failure/partial deployment/Uncommanded deployment will affect the safety of the flight.
* The need to use a drogue chute can limit the crosswind landing of the airliner significantly.
* Aircraft dragging a huge chute during taxiing back to the ramp is not a good idea from FoD point of view.
With the improvement of the brakes and reverse thrust, parachutes are no longer an option for airlines. Nowadays the carbon brakes are the best brakes in the aviation market, together with auto brakes, reversers and speed brakes, most of the new generation aircrafts are landing much shorter compared with old generations, the reject takeoff is almost automatic and with the correct calculation the runway overrun accidents are decreasing considerably. As the effectiveness of the thrust reversers are better at high speed, most of the airlines uses reverser thrust in idle, the pilots are suggested in case of using other than idle reversers, to apply reverser thrust until 80 knots or 60 kts after landing, auto brakes combined with Carbon Brakes and a speed brake, give to the aircraft shorter stop distance than before. The brake temperature is much better in carbon brakes, hot temperatures are still a problem in case of reject takeoff but for long taxis is no longer a problem. So parachutes are retired in commercial aviation. Hope this explanation helps. ;)