I remember the time when Lithium Ion batteries first came out, they promised to offer a better capacity to weight ratio than Ni-MH batteries, but for a long time I could never figure out why they were only available as proprietary batteries and not the usual size AA, C and D cell sizes. Well, one reason is due to the cell voltage - Ni-MH and Ni-CD cells both have a voltage of 1.2 volts per cell, while Lithium Ion and Lithium Polymer batteries both have a voltage of 3.6 to 3.9 volts per cell.
With Ni-CD and Ni-MH batteries, these can take quite a lot of abuse without them rupturing. For example, you can drain the cells to zero volts and can expect them to charge back up again (assuming they are not totally flat for an extended period). Should you leave them in a charger too long which does not automatically cut off, there is also a good chance that the batteries will still work fine and I have often done this by mistake with my old 5-hour battery charger that has no automatic cut-off.
Lithium Ion and Lithium Polymer batteries are quite different and will not tolerate abuse. For example, if a Lithium cell falls to below 1.5 to 2 volts, it can become permanently damaged. Worse still, if a Lithium cell is continuously charged beyond 4.3 volts, it will self-destruct. Lithium batteries also have a much shorter life than Ni-CD and Ni-MH batteries and with everyday use, they usually only last around 1.5 years and is the reason why you may hear about people complaining about their laptop batteries giving up after a year or two. However, with most consumers getting a new mobile phone every year, most generally don’t experience this issue with their phones unless they are a very heavy user. This article here gives some further information on the life of Lithium Ion cells.
With the amount of cameras, mobile phones, laptops and so on that use Lithium Ion or Polymer cells, virtually all of these batteries have protection circuits to protect against excessive discharge, overcharging, short circuit, extreme temperatures and so on. However, if this circuitry fails, this is where problems often happen, especially if the overcharging protection circuitry does not work properly.
To give an idea of what happens when one of these batteries is deliberately overcharged (without protection circuitry), this Google video shows the result of over-charging a small R/C Lithium Polymer battery:
This site gives a few more examples of Lithium Polymer batteries exploding and bursting into flames from overcharging:
(Click on Lipo fires 1, 2, 3 from the left column)
Just a couple of more examples of a laptop catching fire, in this case an Apple iBook (unfortunately no video clips):