Legend of Zelda: Ocarina of Time if i'm remembering correctly. Took me four months at age 8 or 9 when it first came out. It's either that or Super Mario 64...
Wow, this one really makes you think...I don't even know if I can honestly even guess as to what the first game I beat was. It might have been Zelda, Ocarina of Time...and I was so proud and excited.
I think it was the original Sonic the Hedgehog for Genesis/Megadrive. That was also the first console game I ever owned (I'm not counting my parents Intellivision ).