For me it's either Metal Gear Solid or Granturismo in '99. I can't quite remember which order but both were beaten early in the summer of '99 and many games came in quick succession after that. If it was GT it would have taken at the very least 12 months and if MGS it would be no less than 9 months. Before beating these games seeing credits was an impossible task, not just the skills of a nine year old but until the memory cards allowed for the saviour of progression it was a demoralising process going right back to the start. 

Did you manage to beat games before the advent of save data? Did you use some kind of password instead or did you just git gud?

Honestly, I can'r remember.

Probably Super Mario World, since it was the first game I got.

Super Mario Bros. NES.

Sonic the Hedgehog on the Sega Master System, in 1999 when I was 6.

Super Mario World for SNES

It was either 1993 or 1994.

First game I beat was Super Mario Land around 1990.

Before that I played other games, but they were never ending. Pretty sure Heli-Battle was the first game I owned and I still have it.

EDIT: Added boxart!

I think it was Pokémon Blue.

Wario Land: Super Mario Land 3. I love this game...

Mega Man 2.

But most of the time when I was young, I kept playing the first level of a game over and over again because everything else was too hard for me. =D

The earliest memories I have of gaming are Crash 3 and Super Mario Land 2.

I almost certainly had the Gameboy first, but I'm unsure when I beat it. I remember discovering the easy mode and that's how I managed to finish the game as a young child lol.