Critical hits. There are lots of different mechanics from different systems, but the ol' default always seems to be 20 always hits + critical effect, and a 1 always spectacularly fails.
Statistically this seems to be stacked against the players. They are usually the few that fight the horde. So if every roll has a 5% chance of not only hitting no matter what but doing extra damage on top of it that horde of goblins is suddenly a bit scarier (not really, but mathematically they are fearsome!) That 5% comes up a lot more too but no one really cares if a goblin drops his sword. There are too many to deal with anyway.
Yet players love Critical hits. As a player I love critical hits. I think the first rule we tossed in 3rd edition D&D was the confirming a critical nonsense. Don't deny me my criticals!
After all this is the stuff those great gaming stories are made from. In one game the DM introduced us to the big bad (a vampire). We weren't supposed to beat him, weren't really supposed to get into a fight at all, but we did. The plan was we were to be defeated, learn a bit of his plan, level up for a while and then climatically defeat him at the end of the campaign.
What really happened though....
We descended into the cave and started to battle the big bad. A few rounds in we realized what we were fighting. We didn't have magical weapons, not a lot of magic, and realized we were outclassed, we didn't even realize how badly we were outclassed. My wife who didn't have a lot of D&D experience at the time, said she was making a called shot with her crossbow at his heart, because stake through the heart works on vampires right? I cast true strike on her because it seemed like the best option at the time and then she rolled and got a natural 20. The DM decided it didn't matter if undead "couldn't get critical hits on them" The bolt few true, pierced his heart and killed him. High fives went all around and the tale is still told to this day (outside this blog as well!) The GM let us kill the big bad early, because it was just too cool an opportunity and the dice were on our side along with a good plan, who was he to let a little rule get in the way of a good time and sharing in player success. He just pencil whipped in that the real big bad was a deamon or some such, and we fought it later.
So on the other side of the screen now I keep critical hits around for just that very reason. I've expanded a bit on the critical fails as well.
I ran a group through Keep on the Boarderlands. It was the one time I was planning on having them encounter orcs and goblins and such so I put in a bit more thought than normal to the cannon fodder.
I did this by expanding the critical fails. Whenever the goblins rolled a 2-5 I aborted their attack and had them do something rather goblinish. They would loose interest in the battle and take a nap, stop and pick their nose, get confused and think that they were retreating only to realize that they were wrong and come back next round. I saved the dreaded 1 roll for them getting some revenge on another goblin and taking the thick of melee to stab the other one in the back while no one was noticing.
I played it for laughs and the players seemed to really like it. Looking back I think it added more personality to the monsters they fought rather than the normal swing and miss, swing and hit results from the dice.
I liked this so much I expanded this to other monsters, though I ended up reducing the numbers to 1-3. So whenever this came up I use the opportunity to have the monster do something to show its personality (after all the players aren't going to sit down and have a tankard of ale and get to know them anyway). They may boast, or gloat. I'll have the monster give a "tell" in a round as a precursor to using a special ability, like a dragon taking a deep breath as the round action prior to using its breath weapon.