If we are listing one experience per game system (and not counting arcades), here is my list.
1) Playing 4 player Warlords and/or two player Combat on the Atari 2600 with my parents and siblings as a family after watching the Sunny and Cher show and/or The Muppet Show.
2) Playing hours of Moon Patrol by myself on the Atari 5200 on my grandpas hand me down black and white TV in my parents guest room.
3) Having Japanese exchange students that brought over a Nintendo Famicom and getting to play it.
4) Working for my dad all summer long to save up to buy a Nintendo Entertainment center. All my friends had one and my dad told me that if I wanted one, I would have to save up and buy it myself. So I worked for him all summer and with a bout two weeks of summer left I had enough to buy it. I then spent the next two weeks playing The Legend of Zelda non stop (that was a very special time).
5) Getting a Nintendo 64 in my early 20s when I had roommates. We would get trashed and play Mario Cart all night. That and 007 GoldenEye on big head mode with paintballs.