Alyx greets Gordon with a huge hug at the start of Episode One.
Let's be honest - virtually every single interaction with Alyx is an exercise in Heartwarming. She's just that nice.
The fact that humanity is still fighting, even after twenty years.
At the very end of the Ravenholm Mines, there is a minecart trap that includes a spinning blade, which you use to kill the remaining zombies before escape. If we think about this, Father Grigori managed to swim through the Ravenholm mines, climb over fences that Gordon can't climb over, and fight the infinite horde of headcrabs, all twice just to help any rebels that come by and to tend to his flock. He could have left, seeing how close he was, but he didn't. Also counts as Awesome.
The original credits theme for Half Life popping up in Half Life 2's credits can be pretty heartwarming for someone who finished both games.