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Promethean: The Created is the only game in the New World of Darkness to have anything approaching a predefined "happy ending"... but as this is the World of Darkness, it's a long road to hoe. Prometheans get some of the worst Blessed with Suck of all supernatural types — they come into existence in adult bodies with undeveloped minds, their very nature makes humans flip out and want to kill them over time, the very earth rejects them, and since they're so rare (for obvious reasons), it's hard for them to band together in groups. But as they're unfinished works, they can undertake a long and arduous Pilgrimage to figure out what humanity is... and, in doing so, become human themselves.
The worlds of Changeling or Mage don't have quite as defined a "happy ending", but the games stress over and over that despite all the doom and gloom, there is a very real chance that a Changeling CAN reconcile their trauma and live out their lives in relative peace, and that Mages truly CAN make the world a better place if they avoid the pitfalls of hubris.
Mummy: The Curseturns out to be the second NWOD game to offer a possible "happy ending". The Arisen can seek Apotheosis, reclaiming their freedom, their selfhood, and their memories from the Judges.
The Time of Judgment, the series of supplements that originally finished the Old World of Darkness lines, included multiple scenarios where the players have the chance to overcome the World Half Empty and earn their happy ending (for themselves and for the world, even).
In Wormwood, one potential resolution for a Vampire: The Masquerade game, the player characters are offered a shot to atone and seek redemption as God judges the ultimate fate of all vampires. That is, if they can last 40 nights without succumbing to their beastly nature...
Judgment, a scenario for Mage: The Ascension, covers the last moments of reality. The players will be entrusted with the means to save the world from total destruction... But in the path to achieve this goal, terrible secrets will be revealed, friends will turn again each other, institutions will collapse, nations will be thrown into anarchy, monsters will be freed to roam and feed, and millions upon millions will die. There will be too many chances to fail as magical wars ravage around them, cosmic forces hunt after them and inner weakness and flaws will surface to haunt them... But, if they fight for everything and manage to fix the error that made the world a world of darkness, all of humanity will be freed from the shackles of doubt and disbelief and Ascend. Hard to ask for a happier ending for the entire universe.
There are a number of scenarios for Werewolf: The Apocalypse where the much-feared Apocalypse comes to pass... and just as many that say, "If you knuckle down, atone for past sins, and strike true, you will win against the Wyrm." The 20th Anniversary edition reinforces this, with a comic where the Prophecy of the Phoenix (the account describing the Apocalypse) is reiterated... only for a new clause to appear, effectively saying, "But if you stand and fight instead of wallowing in hopelessness, who knows what'll happen."
Exalted has The Return of the Scarlet Empress — a campaign detailing the culmination of the Reclamation Conspiracy. The final climax includes the Ebon Dragon, the Yozi who created the concepts of misery, vice, cowardice and evil, returning to Creation and attempting to install himself as a fundamental aspect of Creation. The Exalted heroes, unlike the time when they combined their heroism and strength to defeat the Primordials, are shattered and turned against each other. The Solar Exalted, the most mighty of all, are only young and weak. Creation has been ravaged for decades by the demonic forces of Hell... But if the Exalted stand against the Yozi and fight with all their might, they might — might — defeat the invaders and protect Creation from another apocalypse. But it will be a bloody fight where giving up seems to be the comfortable and sensible option...
This is Exalted as a whole. The challenge isn't saving the world from horrible monsters, it's saving the world from yourself and/or making it a place worth saving.
Feng Shui models itself on Hong Kong action movies. And as anyone who's seen a Hong Kong action movie knows, the heroes are not guaranteed to win the day or get out of things alive — in fact, tragic endings are rather common in Hong Kong cinema. So while happy endings are indeed possible in the world of Feng Shui, you're going to have to go through hell to get them.