Bags of polymer fun

What you need:

A plastic carrier bag.
A pair of scissors.

What you do:

Use the scissors to cut a nick in the carrier bag, between the handles. Try to tear the bag from top to bottom - it's very easy, right?
Now cut a nick in the side, and try to tear it from right to left (or vice-versa). Hard, eh?

What's going on:

Carrier bags are usually made out of polythene, which is a polymer - long chains of carbon atoms. The chains mostly line up, and 'cross- link' to each other.
However, those cross-links are much weaker than the immensely strong bonds along the chains. Thus, while it's easy to separate the chains (tear down the bag), it's harder to split them in two (tear across the bag).
Why, then, are the chains arranged vertically in the bag? Because the chains are much stronger along their length, so the bag can carry a heavier load without stretching.
Most of the time, that works very well. But the designers of carrier bags are nevertheless making a trade-off, since even a small tear in the bag can cause a run, separating the chains. And we all know what happens then.