Once, when I was a kid, I had an AA battery sitting on a bookshelf on it's side. I was laying in my bed, reading a book, when there was a loud !BANG! - it sounded like a small firecracker. I got up, and found the battery had shot the positive end (with I think the rod - which would make it a carbon-zinc cell, IIRC? I can't recall exactly...) off the battery across the room, where it hit the wall and bounced off of it; the body was still on the bookshelf.
LiPo batteries, though, are a known fire hazard - while charging, being exposed to heat, etc. In the R/C world, they sell special fireproof bags to charge LiPo batteries in. There's pics out there of people who've had fires because they overcharged their LiPo packs, or they charged them in a way in which the heat couldn't escape properly (this kind of thing caught a dorm room on fire at some school when the student was charging their laptop inside their laptop bag). Recently on Reddit there was a posting where a GPS device, mounted to the window (via suction cup mount) of what appeared to be an SUV, was left out in the sun, and the battery heated up, caught on fire, and ultimately burned up the interior of the car before it was put out. So you gotta be very, very extra careful around LiPo batteries.