Recently, there were articles and pics of a laptop exploding into flames at a conference in Japan. (It was a Dell, but the brand is not important-really.) The preliminary results of the investigation point to the battery itself as the culprit, which is why I say the laptop brand doesn't matter in this.
The link above will take you to an article in which Lithium ion batteries caused a fire when they were being shipped. They weren't even in use!
Obviously, our favorite battery technologies have some safety problems. Research is ongoing. But what happens when a laptop goes incindiary in a crowded aircraft passenger compartment? Aircraft fire fighting systems are not geared to a fire of this type, according to everything I have read. (And, no, I don't understand that, either.) Are we going to have to give up our favorite electronic devices on board aircraft? This report indicates that just having them on the aircraft, whether in the passenger compartment or in the cargo hold, might imperil the aircraft and (more importantly) the people inside.
The number of fires attributed to this type of battery is reassuringly small, but the potential for a real disaster is certainly there.
In checking this out, I've found out that not all battery research is about extending charge life and such. A decent fraction of it is dedicated to safer batteries. I didn't find news of any breakthroughs, but they could easily be making incremental progress and I missed it.