Majora's Mask gave me that feeling many, many years after I first played it. I spent a lot of time as a kid playing it with my uncle, and when he passed away I felt compelled to return to it and play through again. The themes are really powerful, and the idea of taking on the identity of the deceased and essentially carrying on their legacy and fulfilling their wishes is... powerful. It's an incredibly powerful game.
Portal 2 made me say "WHAAAAAT" out loud a few times, mostly at the mid-game twist and the ending boss fight. Just ridiculous. The achievement sums it up really well: That just happened.
Gone Home reminded me of what it was like to be young and full of love and naivete and fear and uncertainty. While I was not in the same position as the characters in that game, the emotions that were touched on were extremely familiar.