- a regular day in the job as a fatebinder goes wrong when your boss gives you an impossible deadline on your current project. Now you have 8 days to deal with the rebel scum, all the while trying to get 2 separate and feuding departments Pillars of Eternity
- A casual pit stop by a caravan goes wrong when everyone else gets slaughtered while you went for a strode. A magical wind then hits, which leads to you taking shelter in a temple where you run into a bunch of cultists doing some sort of magical experiment. As a consequence of being too close, your party is killed while you are given super powers. Pillars of Eternity 2
- Your castle from the 1st game is destroyed and you get stepped on by a giant foot of a resurrected god. You are brought back to life by another god to deal with this aforementioned rampaging god. You wake up, resurrected, only to have your ship attacked and beached by a scumbag pirate named Ben. Fallout
- after the initial cutscene intro, you are immediately placed into the world outside of Vault 13, and are free to roam the world to to progress your main missionFallout 2
- you begin the game completing a final rite of passage, a final test prior to accepting your mission in the outside world that will let you save your vault. Fallout 3
- you are given your protagonist's life story (literally), and then dad goes out for a pack of cigarettes and doesn't come back. Your vault isn't happy about his choice to leave and decides you should be the one punished, forcing you to leave the vault into the outside world in search of father. Fallout New Vegas
- a regular day in the job as a delivery person goes wrong, and you take a bullet in the head thanks to a scumbag named Ben. You are rescued by a robot who brings you to the village of Good Springs. The village will soon be under attack by a local gang, and you have the choice to help either side, or beeline towards Vegas to hunt down Ben. Neverwinter Nights 2 - Mask of the Betrayer
- you awaken in a place that you must escape from, with an affliction that seems impossible to get rid of, but will ultimately kill you in time. In the meantime, it does grants tremendous power, and drawing on this it causes you to manifest tentacles and eldritch imagery. The true source of this affliction is unknown, but there is strong hints that it is a results of the machinations of Myrkul, one of the Dead Three. Your first companion is a female belonging to an organization with a reputation of being morally dubious in the Forgotten Realms. Oh, you are also in possession of a powerful Gith artefact which may be the key to solving this whole plot.
Shadowrun: Dragonfall - Run goes bad, survive until you figure out what's what.
Shadowrun: Hong Kong - Your step-father asked for help, and now you're wanted by the police in a foreign country.
I absolutely loved these two intros, especially Dragonfall with the heist gone wrong. They do such a good job introducing the tone, the world, the cast, and the motivation behind the story.