http://www.nytimes.com/2009/01/04/magazine/04risk-t.html
The problem, basically, is asymmetrical payoff. 99% of the time, the payoff was big, and worth the risk. 1% of the time, it caused a catastropic meltdown.
Taleb, Our Lady's Non-Prophet for the 21st Century
Not to besmirch NT, but there seems to have been a few other problems at hand; GIGO, insufficient data, and the map/territory thing.
After all Goldman Sachs used VaR, but they noticed something weird was happening; so they went conservative, shored up their accounts, and missed the worst of it.
In short, it wasn't completely the VaR in itself, it was also that it was used improperly.