I have been flying lipos since 2006 on the other site in the battery fourm you can find several sticky threads (lipo fires are real & complete guide to lipo batteries and failure reports part II )
The guys over there have done an awesome job of keeping track of pack issues and fires. You can read story after story of lipo fires.....
The one thing you will have a very hard time finding is a story of a lipo lighting on fire when it's just sitting there undamaged in a storage charge.... in fact you won't find one report. There is always something that may be an issue.
I'm not saying you should feel they are completely safe... there is danger with all fuel we use to power our planes.

Always balance charge
buy high quality chargers and lipos (almost all lipos chargers now have a built in balancer)
always charge outdoors in a safe area
discard all damaged and puffed packs or if you have one that won't stay in balance anymore get rid of them (don't be cheap..lol)
Keep packs in storage charge in vented ammo cans and lipo sacks

The beauty with todays fast chargers like the FMA power lab 8 is I can charge at 40 amps..... so I can show up to the field and start my chargers and have 4 -6s 5000 mah packs charged in 25 minutes. So by the time my planes are setup the packs are done.... I hardly even charge at home anymore. Maybe just a few to start my day and the rest at the field where its safer