Pokemon Blue maybe. I don't think I got good enough to beat other games like super Mario.

Super Mario World is the first one I remember beating.
That game took months for me and my lil bro to get through.

I had a Commadore 64, and remember playing alot of games before the SNES (when I was young, but don't recall beating any of them).
We played alot of NES games at friends houses too, and might have beat a few there as well (maybe mega man games? or the super mario nes games?)

But the first "real" standout memory of a game being beat, single-handedly (mostly) was Super Mario World, on our SNES.

Pitfall 2 on the Atari 2600. What an amazing game that was for its time.

Adventure on the Atari 2600.

Scott Adams's Pirate Adventure on the TRS-80.

Mario 1. I think.

Back in 1994 my couisin got an SNES and gave me his NES with Mario 1, 3, excitebike, and a couple of other games. I said I think because I vaguely remember beating Mario 3 1st.

It's something on the NES, but I'm not entirely sure what. Either Mega Man 4 or Kirby's Adventure, I'm guessing.

Probably Super Mario Land.

Isn't it strange how we can't remember, it should be something that should be solidified in memory like the first day at school. I can remember a random day in 1993 as a three year old but I can't remember achieving something so massive at nine years old and try as I might I can't put the years in order. I remember the joy of beating those first few games but I can't remember what order they were or even where I had my playstation and TV setup at the time, now that I keep thinking I might have beaten Granturismo in 1998 but I can't remember if I just got really far into it or I actually beat it and there's also Time Crisis which I beat many dozens of times but I can't place it at any date, it could have been any year from 97 to 2000 for the length I had the light gun. That's most likely my first completion cause I could beat it in one sitting without missing a head shot so I obviously put in the work, I just can't remember even a day of practice or any failure. 

The Secret of Monkey Island on PC