Heartwarming / Europa Universalis

• Anytime you ally with a country that you won a war against. It takes a few years and a lot of money, trade, and royal marriages, but eventually that same country can become your best friend.
  • Especially if you do it with England and France, or Castille and Portugal.
• Peacefully integrating another country via royal marriage and then personal union. Sure you could conquer them with your armies, but sometimes love and charm are more effective than sword and cannon.
• By that same token, as a colonizer you can sometimes go out of your way to treat the natives well - for instance, sending doctors to help treat the diseases your settlers brought with them.
  • Taken further in IV's The Cossacks DLC, which allows you to choose from three native policies how your realm should interact with the natives. Picking native coexistence reduces the native uprising chance by 100%, meaning natives will never attack your colonies, which is both heartwarming and very practical.
• Starting as an oppressive nation (e.g. Muscovy or Castille) and turning them into a free, forward-thinking state, even if you have to drag them there kicking and screaming.
• Any event that mentions how awesome your nation is. Try not to feel proud of yourself when game tells you that other nations envy the bravery of your soldiers, look up to you as a shining beacon of culture and progress or simply employ your people because of how incorruptible they are
• The event in which your ruler marries a commoner and doesn't care what the nobility think of it, because he loves her, and the common people soon do as well. Aww.
• The event where your people demand your ruler set aside his wife because she is a heretic or heathen can potentially become this. If you refuse to set her aside, showing loving devotion that transcends sectarian differences, then a province in your realm that also shared her faith feels comfortable enough to become open about following it.
• While playing most indigenous nations that historically got crushed by colonizers and preventing that from happening probably counts, special mention goes to the 'No Trail of Tears' achievement. Playing as the Cherokee, you have to control and have cores on all of the Thirteen Colonies with all institutions embraced. Stopping the horrors of colonialism in a game all about subjugating natives and building an empire on the backs of colonies is possibly one of the most heartwarming things in the game.
• Being in a tributary relationship can be this, if your overlord actually fulfills its promise of protecting you; unlike other types of overlordship, a tributary overlord does not prohibit its subject's diplomacy, merely taking a token tribute in exchange for protection. In gameplay terms, this means that you can expand as much as you like, and your overlord will protect you from any coalition that forms. At least, the potential of their involvement will.