Gizmodo is reporting on a new battery under development that while based on Lithium technology does not have the same (admittedly minor) risk of exploding that the current batteries have. At the moment it is a ways off from hitting the street, about 3 years, and doesn't hold the same level of charge as current batteries do.

The alternative option that is being worked on is hydrogen fuel cells which may be starting to be available around the same time this battery hits the streets. While hydrogen hasn't always had a non-explosive reputation fuel cells don't really work by burning, and hydrogen is not as volatile as lithium when it combusts. I remember from science class at school igniting bubbles of hydrogen to demonstrate its combustion. This was then compared with a video of lithium being dropped into water. Slightly different scale of reaction there.

While it looks like the basis of a good idea I don't think people are concerned enough about their laptop burning to sacrifice battery life, and it might be a bit too far off to make a difference.