Most places now use natural burlap and many times it is treated to resist decay. When the twine and burlap is left tied you will rarely be planting the tree at the proper depth. most B&B plant are 3-6" deep in the root ball, if you don't remove the burlap you will not find the root flare. If you don't find the root flare you will rarely get the proper planting depth. I've seen a 100 times more trees that died from being planted too deep than ones that have been girdled.
When the burlap is left on it acts as a wick and will dry the ball out and reduce the amount of water moving from adjoining soil to the root ball.
Jay mentioned 3-12 years for the burlap to decay, that is correct in many cases. Last month I removed a maple that was planted 15 years ago. The wire basket and burlap were still present. I once removed at taxus that had been planted 30 years earilier and still found burlap in the bottom of the hole.
Remove the twine, burlap, basket, etc from the top half of the rootball, minimum, PERIOD!