I've got lots of memories, but rather than making a bad/mediocre game memorable, it just anchored associations in my head.
I remember the day I received Mario Land 2: 6 Golden Coins, back when it was current (when dinosaurs roamed the earth), my parents had taken my sister and I to a glass factory/museum. I don't remember a damned thing about the glass place (yawn!), I do remember coming home at tea time, mum and dad having a blazing row and a small yellow package on the mat for me! It was a massive step up from the first game with beautiful tinny music and a Ducktales kind of vibe.
My Dad's aeroplane mad, when I was a kid it was all a bit of a mystery to me, they were just flying lumps of metal with different shapes and names. I'm not huge on planes now, but I know the difference between a Mosquito and a Phantom II. We did start with PCs during the late 80s, one of the handful of games we got was Chuck Yeager's Air Combat, which my dad loved, over time I started to play it and mess around with the planes' flaps and gears, eventually getting quite good at shooting down bombers and dogfighting. I rather foolishly got rid of our old PC games years and years ago, but a few years back I spotted a complete and good condition copy of the game for the princely sum of £1 at a car boot, so it sits proudly on my shelves once more
The Legend of Zelda isn't something I'm a massive fan of now, but the early games are absolute gems. My friend had the NES and SNES games, we used to play them all the time. I had the chance to get the current one when Link's Awakening was released - I had a gameboy
I can remember Mum driving me to the nearest town one evening to pick up a copy from Woolworths, bless her.
D/Generation was a game we had on our crappy first PC, with CGA graphics (16 colour, all pinks and cyans). It closely resembled the games I had been playing on our Spectrum, but it was a step up in terms of complexity, plot and graphics, I felt very grown up playing something so well put together. It's another one I've managed to reclaim, it's one of my favourites.
Pippo for the spectrum is one of my earliest memories, Mum loves it too. It's basically Q*Bert, but on flat grids rather than pyramids. Despite being developed midway through the 8-bit computer lifecycle (1987), it was one of the most colourful, musical and sonically powerful games on the system. Later on, when the 8-bits were struggling to keep up with 16-bit computers, things like colour and music were dropped to save memory for larger, more complicated games. Here's a youchoob video if you're interested:
https://www.youtube.com/watch?v=_QU3c9nOWTY