Depends. Not even just varying that much from genre to genre.
if i were to play Metal Gear Solid 4, then i think i'd see it as complete when I finished watching the last cutscene (having just done the last battle of course before i get youtube linked the final cutscene

)
However, i didn't consider myself done with Metal gear Solid: Peace Walker until i had gotten S rank on the majority of the missions.
Another example would be Final Fantasy 4 and Final Fantasy VII. I beat Sephiroth. I beat FFVII. I'm not too worried about the emerald weapon raging around under the sea. Final fantasy 4 on the otherhand, i wasn't done with until i had done everything i knew was possible on the game and could literally pick the four characters with the lowest attack and beat the final boss by closing my eyes and pressing 'a'.
So basically, until i'm bored with it or see no point to play anymore. technically i'm still not done with my FFIX or X, because i'm still picking those up every so often.
oh, and note that whilst playing Pokemon Pearl i did say "There, i've completed the game. The End. No more for me" after beating Team Galactic. I saw little need to continue, I had saved the world and had heard my last Team Galactic Admin music.