Games where you, the player character, was charged with saving the world and failed spectacularly. Now either you need to try again, or another PC has to clean up your mess. Mainly so the developers have an excuse to justify the sequel.
The Commander (XCOM: Enemy Unknown/Within and XCOM 2): No matter how well you play your game in the first XCOM, the plot of XCOM 2 establishes that you lost the war. The aliens announced themselves to humanity and tricked everyone into thinking they were friends, not foes. The world governments welcomed the aliens with open arms and turned on XCOM, giving up the location of your base and allowing the aliens to capture you. The sequel started with your XO from the previous came, Bradford, leading a mission to rescue you from the aliens, giving you a second chance to save the world.
Anduin Lothar and Orgrim Doomhammer (Warcraft and Warcraft 2): Though Warcraft allows the player to play as both orcs and humans, the protagonist isn't named and there are two scenarios where orcs and humans win. The human campaign ends with the orcs being hunted down and run out of the kingdom, while the orc campaign ends with the orcs razing the kingdom of Azeroth and making plans to take over the rest of the world. Warcraft 2 brings a bunch of new lore and retcons into the setting, and it establishes that the humans lost the war. The human PC, Anduin, took the surviving humans north to a new kingdom to beg for aid, leading to the creation of the Alliance. Meanwhile, the orc PC, Orgrim, finds allies and creates the Horde. The events of the next game document the second war between orcs and humans, as well as their respective allies.
Hawke (Dragon Age 2 and Dragon Age: Inquisition): Hawke's goals in DA2 involve protecting the city of Kirkwall from everything and everyone who would harm it. No matter what actions the PC takes, Hawke fails this goal. Hawke spends the whole game trying to stop a brewing conflict between mages and Templars in the city. But eventually, a mage blows up the church and provokes the Templars into attacking the mages. Hawke can either try to protect the mages, or aid the Templar in slaughtering them all. But regardless of what happens, Hawke is run out of Kirkwall while mages and Templars go to war. The plot of Inquisition starts with the Inquisitor picking a side and ending the war.
(Also, the big bad Hawke kills in the DLC shows up to be the main antagonist in Inquisition. Because Hawke isn't allowed to have nice things, apparently.)
The Game (ye olde millennial meme): You lost. Again. Good day, sir.