FarCry is my favorite game so I've finished it many times, learning new tricks each time. The fastest I've completed the game is 2 days in perhaps 8-10 hours of actual gameplay (sorry didn't keep track exactly). My skill isn't bad but many (younger) folks are a lot better.
Somewhere there is a video of a guy finishing HalfLife in under an hour (WoW)!
So post your best times for your favorite games here!
This may be a little cheap, but I once bet a friend that I could beat Sonic The Hedgehog 2 in less then 5 mins.
Go directly to last boss and then mashed the pause button to play in slow motion on the boss. This made it take about 30secs longer but guaranteed that I wouldn't die and have to start over. I think my total time was around 3mins.
Since your title includes *any game*, my best time to take a WoW toon from 1 to 60 is perhaps 9 played days (that work out to be 9 x 24 hours). I forgot to take down the statistics of my leveling from 60 to 70. But I read from the news that one guy managed to reach from 60 to 70 on the first day of launch in ... just 1 day ...
... with the help from 40 ppl in his guild. He had a team of people helping him to finish the mobs that he tagged (so he gained the xp) and another big team of people non-stop running the entry level dungeons to reach a decent level in order to help him finish the near level 70 mobs in the later half of the day.
But just because you finish a game fast, it doesn't mean you're really good at games. Some games are way too short. E.g. The Baldur's Gate games take about 100 hours of gameplay - now that's getting your moneys worth!
Yeah I know not every game can take that long - but I think 10 hours is far too short. All games should take at least 30 hours, IMHO.