For all of you who point to cell phones, laptops, etc - Sony and Dell (and probably others too) had a massive recall a few years ago on battery packs, after a series of fires (2005 - 2006 time frame, IIRC)
Boeing got into issues more recently with the batteries on the 787, as did GM with the cells on the Volt (and Toyota went back to NiMH on the 2nd gen Prius because of failures during prototype testing, again, IIRC).
Air freighters have crashed due to Li batteries exploding during transit - pretty sure the crew wasn't busy over charging them at the time either...
I've had a tank almost go up in my lap after I wired up the circuit wrong (fastest battery disconnect in history right there!) - the battery took all of about 3 seconds to get the insulation on the cables producing enough smoke to scare the crap out of me, I'd guess 10 to 15 secs would be all it needed to start a nice fire if I had let it carry on...