Three examples.
First is a new wild mage PC I had just rolled up. It's the first round of the first combat of the campaign. I cast a spell - wild surge, a 1 in 20 chance. DM asks me to roll percentiles to see what happens, then cackles. Asks me to roll percentiles again. I roll really high. He laughs some more, then starts to explain. Turns out my wild surge was "caster polymorphs randomly" and I had turned into a chipmunk. The second roll was to see if I kept my mind, a rule from earlier editions - there was a chance you wouldn't remember what you used to be when you got polymorphed. I failed it badly. So, first combat action of the campaign, my PC turns himself into a chipmunk and bolts into the woods, never to be seen again.
In another group entirely, it was the first session of a sci-fi game. We were on a ship that was falling apart, and had to escape. I'm a big lug of a fighter, carrying the power source we need to get an escape craft working. We get into a firefight, and one of the genius PCs throws a grenade at my feet, trying to save me from a couple of mooks. Blows up, knocks me and the mooks out, and breaches the power cell I'm carrying. It starts beeping, and after a couple of bad rolls, blows up while the group's tech is trying to fix it, killing him and tearing a hole in the ship that kills another PC. The last PC is left on the unpowered escape pod and eventually eats a bullet before burning up in atmospheric reentry.
Third was in an Alternity colonial fantasy game I was running. One of the PCs was a dhampir, a half-vampire. He's been struggling to control his urges, and gets wounded enough that he needs to feed. It's a willpower check of some kind to resist the urge to kill, and he botches it - a natural 20 in a roll-low system. Kills the guy he was just trying to drain a little bit and leave relatively unharmed. As a dhampir, killing is addictive, so I have him roll another willpower check. Another critical failure. He goes tearing off into the night to find more victims. Ends up killing several people and losing a whole lot of progress on fighting his addiction because of a few bad rolls, almost becoming an NPC.