Having an Elder Sim die of old age in The Sims 2 at gold or higher aspiration. They're greeted with zombie hula dancers, and Death greets them with a cocktail and tells them they're going on an eternal vacation.
Various patches for Sims 3 occasionally add some pretty significant things beyond just fixes and minor feature changes/additions (stairs over gaps? Yay but unlikely to change your world). For example, one patch added in new animations... including a whole set of child/toddler animations thus allowing them to hug, have the child feed the toddler, and play peek-a-boo. D'awww...
Many of the quests in Medieval are very, very silly...but I defy you not to go "Aaaaaw" should you decide to send your Peteran Priest off to soothe/convert the resident rabid chinchillas (as opposed to the "Kill their furry bahookies" approach). At the end of the quest, you get a cute graphic of some enlightened and reverent chinchillas along with this final line:
The docile chinchillas roamed out into the sunlight, calm and serene. Prior (Whatever-his-name-is) smiled at them and they - like old friends - smiled back.
You may melt now.
Any of the quests where the intent is to get the monarch married could count as well.
As well as any quest where there is a threat to the kingdom that allows you to peacefully remove the threat rather than outright kill it. Not to mention most of these "threats" had no intention of harming anyone in the first place.
The last "story" of this trailer, with the dog, the kid and the bullies.
In Sims 2: Pets, it's possible (but very hard) to befriend and adopt pet wolves.
In Sims 3: Pets, whenever a pet dies: The Grim Reaper shows he loves pets. For example, he hugs a dog or a horse when it dies and cuddles with the kittens. I mean really, just watch this.
Even in the first game there were hints of this. If free will is on and a parent is left doing nothing while their child is asleep, they will sometimes go tuck them in and kiss them goodnight. Awww!
In Sims 3, whenever a couple is sleeping together in the same bed, sometimes one will hug their spouse from the back. It's so sweet and heartwarming.
When a parent gets home and one of their children runs to greet them with a hug. It's a giant aww worthy moment.
except for the minor fact that they will drop their entire list of queued up actions to do it, very annoying when you had a long string of them.
When a child is crying in Sims 2, you have the option to send an adult over to console them.
Generally any interaction between a child and their parent or a child and their toddler sibling.
In the Pets expansions, if a Sim's pet loves them enough, they have a chance to save them from the Grim Reaper.
Reviving Erik Darling in The Sims 3 could be ruled as this.
The Generations expansion pack for The Sims 3 allows teens and older to read bedtime stories to sleepy children. After the child falls asleep, the older Sim will tuck the child in and give him or her a goodnight kiss.
The beginning of the intro cutscene in Sims 3 where a father is flipping pancakes and the daughter feels her pregnant mother's belly, then they hug.
The cute picture in the Goth family album in Sims 2 of teen Cassandra playing with baby Alexander while their parents look on fondly.