Sometimes when I connect my MacBook Air to the charger, the charge light on the MagSafe connector does not come on (and System Information says the power is not connected and the battery is not charging). I tried using a different charger and the MacBook charges fine. What might be the problem?
In my case, the problem was the temperature of the charger. Since it's currently winter in the southern hemisphere, removing the MacBook from charge causes the charger to cool down (since it apparently draws very little mains power when there is no load on the MacBook side). At some point when it is cool enough, it will refuse to supply power when the MacBook is plugged in again.
The workaround is to warm up the charger (for example, by sitting on it) for a few minutes until the charge light comes on. Then the current running through the charger is enough to keep it warm, and it continues charging.
Update: A year later, after returning from being away for six weeks, my charger refused to work again even after sitting on it. Apple was happy to replace it under AppleCare.