Video game memories: Paperboy
I think everyone who played Paperboy for the Nintendo Entertainment System would describe it in one word: Frustrating. That includes many people who, like me, enjoyed the game.
The premise was a basic one: You delivered papers to your customers. It was all of the other things added on that made it such a memorable game. You had to dodge people walking down the sidewalks, swarms of bees, crazy women with clubs, and even the Grim Reaper. Apparently Dracula fired him after he was unable to stop Simon Belmont in Castlevania. Now he tries to stop little kids from delivering newspapers.
In addition to delivering to your customers, you got extra points by vandalizing the houses that did not subscribe to your newspaper. Sometimes they would become subscribers after that. That is a good business plan: Subscribe to our newspaper or else. It would be a shame if something happened to your property. Perhaps the Grim Reaper went to work for the homeowners association, and is technically a hero now.
I think my favorite memory of the game was trying to pull off the trick of riding between a parked car and the sidewalk. Neither I nor my older nieces and nephews could pull it off. The one who could do it was my four year old niece. Not only that, but she would do it consistently. When we asked her how, she said "I don't know. I just did it." I think those are the greatest memories of gaming in any context.