The first time I loaded up 3D Stunt Rider on the brand new Amstrad CPC464 my granddad had just brought home. Jumping a motorbike over London buses? Epic! (I was 5.)
Playing Operation: Wolf in two player with my friend, sharing a keyboard.
Discovering 3.5" floppy disks for the first time.
X-Copy - the ultimate (well, only) weapon in every teen Atari ST owners arsenal of ways to get free games. Bear in mind that in the late 80's and early 90's, "piracy" was still a thing done by fearsome looking men with missing appendages at sea. We had no idea really what we were starting when we were making copies of each others' games. We were almost always copying copies anyway, as there was still very primitive copy-protection there and it took a wee bit of effort to "crack" some games so they could be copied. Ignorance was bliss I suppose!
PlayStation Formula One. I bought my first PlayStation in 1996/7(?) specifically to play the excellent Formula One. I played it at a friends' and bought it with my very next wage. I've had PlayStations for every console generation since, and still love the series as much now.