I was just observed by my boss and my efficiency report inspired this post: failure.
Every character fails sometimes. GMs tend to dwell on improbable successes. We all know if the character dies on say 01-99 and becomes emperor of all on a 00 there's about a 50/50 chance of their being a coronation of all ceremony.
But characters do fail. Sometimes it's as simple as taking a swing and missing. Other times are more involved, like the cyberjock who HAS to avoid the Black Ice security programs and shut down the evil corporation before the security alarms go off and the goon squads arrive.
Usually we don't care how much a swing misses in a fight. This is due to pacing (fights are supposed to go fast, unless you're playing Hero System or Space Opera), and character investment: i.e. it was one lousy die roll. On the other hand if the character with the lousy luck spent the whole game session sneaking through the Castle of Doom to creep behind a tapestry depicting human rights violations and devil worship to slay the Evil Overlord and misses ... then you bet that character is going to want to know what went wrong ('I mean I hit on 01-99! WTF?!')
First realize that players will argue about failure for two reasons: they want the GM to change the ruling and they don't want to get blamed. Yes it's stupid to blame your friend for blowing a die roll. They are supposed to be random?
The GM can always change a ruling. But then it'd be a success and the main idea is failure so how do you ease the player into losing out? In the first place give them an out. Many unforeseen circumstances could cause a failure. If a die roll has any negative modifiers due to circumstances odds are the failure was out of their control. They slipped on something or some dust got in their eyes. The prosecutor's chief witness might get whacked or otherwise be unable to testify or have their veracity questioned. The doctor could have been looking at mislabeled X-rays backwards and removed the wrong kidney (it gave my doctor a few bad moments and that was just to go after a stone.) Perhaps your computer starts an automated virus scan during a starship battle, slowing down your target tracking.
Sometimes you can shift the blame to another character or even better, an NPC (it's better because very few gamers get a ride home from an NPC.) Maybe a waiter spills soup on you during your delicate negotiations and everyone thinks, "Schlemiel!" If you don't have a convenient whipping person you can also blame it on faulty equipment. You don't have to assume the characters are maintaining gear properly if they don't tell you several times per session or something similar.
Failures can also lead to unexpected successes. I was playing a Kerbal Space Program, a space flight simulator, when I simulated screwing up an orbital transfer. My rocket shot out towards the Mun (Moon). It looped around the Mun and collected a lot of data before returning safely to orbit and landing. Columbus, as another example, could be regarded as a character who flubbed his navigation roll. Have a navigation failure send your character's ship somewhere interesting. have their attempt to download files on Imperial spies fail but because another group is trying to download the same files. The other group comes forward afterward to collaborate on a resistance. As a final example have the character trying to build a fire that fails discover the rocks he's using are two pieces of unobtainium (somewhat explosive unobtainium of course.)