Anytime the number of dudes and dudettes who come back is the same as the number who left base a few hours ago.
Even better: complete a mission, especially the more difficult ones, without any injury whatsoever. There's nothing like imagining the squad being cheered as they come back home, tired but satisfied and able to dismiss any paramedics sent to aid them. Even the base personnel comments on, essentially, how well you're taking care of your soldiers.
Breathing that sigh of relief when a soldier in critical condition is stabilized. They're badly hurt and will probably be out of combat for weeks... but they're alive, and that's what matters.
Alternatively, beating the mission while you don't have anyone that can stabilize. If you beat the mission during the time the soldier is bleeding out, he'll be considered as stabilized and taken back to base alive. You can just imagine your soldiers fighting not just to defeat the enemy, but to save their fallen comrade.
Watching wounded troopers joking around in the infirmary. Knowing that they made it out alive and will be back on their feet is... wonderful.
In the opening cutscence to the first terror mission, one of the fleeing people stops to pull a wounded man out of the way while under attack by aliens. This troper found that heartwarming every time he saw it. It's a shame that he gets eviscerated by a Chryssalid shortly after that...
An odd example, but while the Uber Etheral is quick to criticize most of the alien slave races during the final mission, it's surprisingly complimentary toward the Thin Men.
Having been assigned two soldiers with the same last name, it's always heartwarming to think that there's a couple or siblings out there trying to save the world together. Bonus points if one of them becomes The Volunteer.
This troper had a trio of French soldiers, all with the same last name - one heavy, one sniper, one support - that were never deployed without each other.
And this particular troper had a whole 6-soldier squad that were deployed together on every mission. The Psionic Volunteer sniper of the group, who's appearance was that of an older man's from character generation, pushed the second, slightly less experienced sniper (his "protege", more or less) out of the final room, before doing his duty and saving the world. It was almost as though the game acknowledged his almost Team Dad status.
When a soldier is either killed or knocked out, and one of your soldiers panics and kills the alien who took out their buddy. It's heartwarming to think that maybe that shot was payback.
The Memorial Wall, combining this with a Tear Jerker. It could have been just a plaque on the wall, or a notice board. In this game, its surrounded by shot glasses, with a few pictures posted up on the wall, starting out as a few wallet-size clippings if you've only lost one or two and growing to a full size remembrance with almost none of the wall covered if you're sending troops into the meat grinder. All the while, somber Taps-esque military music plays in the background. It is really touching that in-universe, your soldiers aren't simply anonymous weapons sent into a meat grinder, but comrades who remember their fallen dead. Gone, but not forgotten.
Even more so, with the above in mind: visiting a memorial wall with only a few pictures on it. The fallen are remembered, but it feels good to make sure that wall is kept sparse, and that the men and women under your command are kept alive and well. It's good to remember those who have died in the line of duty, but better that there are many more who can do the remembering.
Skipping the tutorial and very careful play can keep that wall empty. There's nothing quite like looking at the list of men you've lost and finding it blank.