In a perfect world the charger would stop charging when batteries are fully charged. I think we have to separate Lithium batteries and chargers... High/regular price vs cheap. One group would be a safe, brand name products, many bought in LBS, and another group - Ebay and Chinese sellers /even via Amazon website/.
Many of the cheap Ebay products don't have overcharge protection /even if they say they have it on the box/. This is the reason why Lithium batteries have such a bad name. It's a cost cutting move, and if the price is right - people buy it lol Some folks think that it's not a big deal for manufacturer to put some extra circuit, thicker or longer cable...If you add up all the additional 5c to each product - they would "lose" tens of thousands of dollars in potential profits.

Lithium ion battery is kind of a broad term. There are a lot of different designs, different chemistries, different levels of quality. A lot of factors effect how safe a battery is, and how well its going to perform. But, all lithium ion chemistries are more unstable than, lead acid, nickle cadmium, alkaline, etc. All you can really do is stick with batteries of good quality, and retire any batteries that show visible signs of damage.

And, I wouldn't leave one charging overnight in my home, or while I'm not home.

Well, I just learned some things. Catman, what does "go up" mean?

I never thought about it, but now that you mention it, I do remove batteries from charger and charger from outlet when charging is done. I'll keep an eye out for name brand chargers from now on. Quality matters!

I don't have surge protectors, but I have a UPS, which should be even better, I think.

Sorry, better said, "malfunctioned and stopped working properly". The Ultrafire charger must of had an internal short with one of the components. It was heating up hence the smell of burnt plastic. Worse case scenario would of been that if I had not been there to unplug it the charger would likely have caught fire and then ignited the batteries. The other charger I had just stopped working for some reason but likely a failure of a component within the charger. If the charger you use has a semiconductor "chip" ( used to regulate the device ) "those" are the components most likely to fail with a voltage surge. If you live in an area where the power goes out frequently or have partial "brown outs", you should definitely have all of your more expensive electrical devices on a surge protector.

I don't believe I've ever had a multi-cell charger fail. Still those are probably just as likely to malfunction if a good voltage surge comes along. I've read of people complaining that their multi-cell batteries would no longer charge ( or only partially charge ). When this happens usually they will wrongly assume something is wrong with the batteries. Unless the batteries are damaged or really old, 4 times out of 5 it will be the charger that is the root cause.