I use teardrops to protect me against drill imprecision.
If the drill is made too close to the track, the remaining conductive material might be too small to be remain functional.
See this blog entry for more details.
Teardrops allow you to add conductive material to prevent that problem. This actually a problem of confidence in your PCB manufacturer. If you impose the right drill tolerance to your manufacturer, you don't need teardrops. But if you need to save some money on the PCB, reducing drill tolerance can be one solution. And then teardrops are a simple protective method.
By the way, my script is just a quick (and dirty) hack. I recently seen this (and hoping it will be integrated quickly):