Garth Nix's
Old Kingdom series- Lirael and co.'s attempts to bind Orannis fail, and are slain. Orannis lives up to its nickname of the "Destroyer", and continues its quest to wipe out all life.
Star Trek TNG - from
All Good Things - Jean-Luc Picard fails to stop the spatial anomaly from spreading further and further back through time, retroactively erasing everything (assuming Q doesn't just snap his multidimensional fingers and fix everything).
Star Trek (2009) - Kirk and the crew of the Enterprise fail to stop Nero from destroying Earth. Nero proceeds to blow up Federation worlds one after another, eventually leading to the region being dominated by the Romulans, boosted by future technology.
Star Trek First Contact - the Enterprise crew fail to stop the Borg from assimilating pre-First Contact Earth. The Borg then use the planet as a springboard to assimilate the entire Alpha and Beta quadrant, as the Vulcans, Andorians, Klingons etc of the mid to late 21st century are nowhere nearly advanced enough to stop them.
Star Trek The Motion Picture - the Enterprise crew fail to get through to V'Ger, who ends up digitising Earth and everything else in the galaxy.
Star Trek The Voyage Home - the Cetacean Probe's influence causes worldwide devastation, because SAVE THE WHALES(TM) or something.
Star Trek The Undiscovered Country - the Khitomer Accords never get signed. The Federation and Klingons probably end up going to war again. The environment of Qo'nos gets progressively worse after Praxis blew up (totally not a reference to Chernobyl AT ALL), leading to the Klingon Empire either falling apart, or at least having to evacuate their homeworld.
Star Trek Enterprise - after the Xindi blow up Earth, the Sphere Builders keep building their spheres, turning the galaxy increasingly uninhabitable to other species.
Star Trek Enterprise again - the Temporal Cold War ends up getting won by some other Very Unpleasant(TM) faction, such as the Alien Space Nazis*.
Star Trek Enterprise again
again - the Borg decide to hang around after defrosting, assimilating 22nd century Earth, progressing to assimilate the Alpha and Beta quadrant, eventually reuniting with their 22nd century counterparts.
Star Trek Voyager - the Borg assimilate One, gaining 29th century tech, becoming even more dangerous.
*Yes, I know that doesn't really narrow things down.