Dell has recently recalled millions of notebook batteries with Sony cells, and Apple has just followed. Its Web site says: "certain lithium-ion batteries containing cells manufactured by Sony Corporation of Japan pose a safety risk that may result in overheating under rare circumstances."
This is not a new problem: Apple, HP/Compaq, Dell and other companies have all recalled batteries before. Also, it is not exclusive to notebook computers: other products also use lithium-ion batteries. However, the risk is very small. Hundreds of millions of li-ion batteries are shipped every year, so I'd guess the number that cause problems is less than one in a million.
You can minimise the risk of overheating and improve battery life by removing the battery when you use your notebook on mains power.
As iPod owners know, li-ion batteries already suffer from short lifespans, typically of two to three years. The Battery University note adds:
The worst condition is keeping a fully charged battery at elevated temperatures, which is the case with running laptop batteries. If used on main power, the battery inside a laptop will only last for 12-18 months.
Nobody has asked this question yet, but I expect they will, so please comment if you can add useful information.