As the links posted by others indicate, asbestos was used in the construction of the building, up to about halfway up. Then, during the time the towers were still under construction, asbestos was outlawed, and the remaining stories were built with some "substitute."
It's an open question whether the towers would still be standing if asbestos had been used all the way up. Possibly they may have stood. Alternatly, maybe they would have still fallen, but stood for a longer period of time, thus enabling more people to escape.
Either way, the decision to not continue to use asbestos was a political decision, not an engineering one.
I doubt it would have made that much difference. From what I've read, most of the people killed were either above the initial point of impact or were rescue workers who were not, at the time of collapse, trying to leave the building.
When trying to fireproof a structure, there's a tricky design issue of whether it's better to have the insulation over the structure as a whole (in which case heat from a fire in one part of the structure can dissipate into other parts, preventing localized meltdown), or whether it's better to have individual parts insulated separetly (in which case heating effects will be localized, but there's more likely to be a localized failure).
I don't know which design approach was used in the WTC, but both would have been problematical. My guess would be from the pictures I've seen that the former approach was used. Such an approach would be best in case of a fire which was not accompanied by much structural damage (most fires would probably fall into this category). In such a case, all that is necessary for the structure to survive is that the metal-to-metal heat tranfer away from the fire through the ends of the involved beams be fast enough compared to the air-through-insulation-to-metal heat transfer from the fire. Given that the frame of the building as a whole has a very large thermal mass, this would normally not be a problem.
The plane crash, however, created a problem: many structural members were ripped apart. The loss of structural support from such members would not have been a problem, but unfortunately the ends of such members would have had substantial areas of exposed metal. While heat damage to these elements themselves would not have been a problem (they were structurally useless at that point anyway) they provided a means by which heat could be conducted to the elements that had up to that point not failed but which now had to bear substantially greater than design loads.
BTW, I forget the exact figures, but I calculated the amount of potential energy unleashed with the collapse of that building. That was a pretty darned big number.
In the south tower, that plane cut through it like a hot knife through butter before it exploded, I don't remember what floor area it hit at but it was much lower than the first. It was basically like having a 20 or 30 story building with very little support left sitting on top of the rest of the building, I doubt having more asbestos would have made any difference.
The heat at that point had to be tremendous, but even without it I think both towers were doomed and would've collapsed anyway, asbestos wasn't the problem IMHO