Mackenzie Calhoun is a walking one of these, but several actual moments stand out:
Mac led a successful revolt against the alien Danteri before he was twenty years old and drove them off his home planet.
His take on the Kobayashi Maru scenario. He blows it up, calmly explains his decision and gets lauded for it. Shelby is raked over the coals for her immaturity.
His response to getting bullied at the Star Fleet Academy? Fight everyone. And its awesome.
Punching out Si Cwan when he first gets on the USS Excalibur. Then getting Shelby to retract her own argument regarding loyalties. Also a Funny Moment.
His reappearance at the end of Excalibur: Restoration where he attends his own funeral that is simultaneously the launch of the new Excalibur. He even quotes Tom Sawyer as an inspiration for doing so.
Shelby has many of these as well.
Shelby telling Admiral Jellico where to shove it when he attempts to get her to spy on Mac.
eventually ascends to the rank of Captain of the starship Exeter. It is a long awaited heartwarming moment as well due to the fact she has been angling for command since we first saw her on Star Trek: The Next Generation.
Shelby single-handedly not only discovers a plague devastating an alien race is due to an enemy species but prevents a war between the two species, forcing the guilty party to sacrifice the Science Council that was behind the plot.
Burgoyne 172 fighting for hir and Selar's child on Vulcan. Doubles as heartwarming to boot.
