I've never played it but am guessing it's The Last of Us?

Nope, or any other DD site - it's a very famous (and slightly infamous) game though!
Nope, not that either

Is it a classic? What operating system did it come out on?

Enter the Matrix, right?

LOL - that's the one!
Your go!

Let me tell you, that was a good one. I almost began wondering if it's an MMO, but the "slightly infamous" hint made me remember the game.

You start as a simple farmer whose village is being raided. You grab a knife and go killing the raiders first, then get to a nearby town, find out it's been attacked recently as well and so your journey begins. It will take you quite some time, make you a hero of the people and allow your descendant to be a protagonist in a later game of the series.

Diablo?

Never played it, just a quick guess.

Dungeon Siege? He had a fork I think...

[s]Oblivion, this sounds better![/s]

Ah, I think you're right here. "...descendant to be a protagonist in a later game of the series"

Braveland

That was quick. Yep, the first Dungeon Siege it is. Just re-started the game to check, (s)he starts with a knife.
And one of the protagonists of Dungeon Siege 3, Lucas Montbaron is a descendant of the first game's protagonist.

Your turn.

You won a ship in a poker game with a famous pirate, because you cheated better than him. Now he sends head-hunters after you...

I don't know which game is this but it sound awesome and I want to play it! :)

Is it Monkey Island?

Nope, another hint: The name of the ship is Mary, she is 81 years old (at the time you play this part) and doesn't like flying.

One piece the game?