Well for for an example you could do "in media res" for classic D&D campaign, by starting the game in the dungeon, as the party fighter kicks in the door to chamber full of orcs (but not impossible odds); tied to an altar is a frightened child and standing behind the altar, dagger in hand, is an evil wizard.
Action!
(The evil wizard will of course escape via teleport or secret tunnel or the like to be the thorn in the side of the party for the rest of the campaign.)
Most players release what they need to do without the back story. Once they rescue the kid explain they were offered a reward to rescue him and return him safely. If a player insists on knowing what the hell is going on explain as quickly as possible during the fight.
Watch any Bond movie for inspiration.
It works best with heroic campaigns where most people are playing characters which don't need much more motivation than point in the direction of the bad-guy.
It is also useful as a campaign start to bring a mixed party together. Either by with the above example, it goes without saying the party will have been hired by the same person and that's why they are working together for the first time, instant team formation. Or putting everyone in the same situation, your in a tower block thats on fire "what do you do?".
Some players might see it as GM rail-roading the plot since they start in a situation beyond their control... those sorts of players need to lighten up (I suggest slapping them in the face with a wet dish cloth). Besides people find themselves in situations beyond their control all the time.
The alternate start for the same situation could have been the players arriving in town, a man approaching each in turn asking for someone to save his son, roleplaying out the fee, some players deciding they are not interested, DM pulling his hair out, some players wandering off to the tavern, some going shopping, eventually after 3 hours doing nothing really the party sets off to the dungeon. They then scout the place, attack the front but screw up, so the cleric blows all his healing spells before they get to the main battle. Before you know it the evenings over and they haven't met the main villian.
Railroading can be fun, players need to learn to hop on the train before it leaves the station.