AS above Diesel PArticulate Filter. There is in theory no reason why they cannot last 150-200K miles on a car, however it is largely dependant on the type of driving you do (it also effects the oil in your car).
If you are a constant "town driver" using the car for multiples of short journeys, then the *regeneration process never gets a chance to kick in
*Regeneration, is where extra diesel is put into the DPF and the temp of the exhaust system ignites the diesel "burning off" the deposits that the Filter has collected. The Regen cycle can only be performed in optimum conditions - these are Hot exhaust and constant running rate, this loosely translates into 20mins on the motorway/A road above 2000rpm.
If the regen process never gets a chance to kick in, then the DPF will clog, then eventually fail. Another side effect, is that the waste diesel from the failed regen cycles gets dumped into the oil sump. The bad thing here is that the oil will then be diluted by diesel and cause premature wear on the car and will nesseitate frequent oil changes as well (expensive).
So, if you at least get a motorway run every 200-300 miles then you should be fine, if not DPF's are a nightmare.
The above is the reason there is such a debate over running costs of diesel vs petrol. My journeys are all motorway, so i am always getting good regen on the DPF, this means that my oil also last longer between services, and i get less overall wear on the engine.
edit - too slow