For me it was the summer Super Mario Bros. 3 came out. First of all, the movie "The Wizard" really hyped that game up because the game hadn't been released yet and it was the ultimate showdown in the movie. Then I got the game in the summer and I ran down to my friend's house and we popped it into the machine and started jumping and Racooning all over the place. He had a homemade Slip 'n' Slide set up in his backyard and as we took turns playing, we'd slide down the plastic sheet, run back up the hill and into the living room to play our level. By the end of the afternoon, their normally light blue carpet was brown with mud and bits of grass was all over the place.
One of the first games I had waited for the release date was Secret of Evermore. I remember I gave my mom some money to go and buy it while I was at school that day and when I got home I blew off my homework to play the game instead.
Centipede on the Atari 2600 was the first time my legs went numb from sitting and playing a game for too long. Actually, it was fortunately one of the last times too.
When my friend bought Metal Gear Solid, I used to jimmy the window to his apartment open and climb in so I could play it while he wasn't around.
Honestly, as I'm sure with most of you, I have way too many intense nostalgic moments associated with video games to list here. That was just a few.