The advent of browser and mobile gaming has made metric/statistic based game design quite popular where you balance your game iteratively based on live player data.
For example if you learn that 80% of players reach dungeon level 4 but only 20% get to dungeon level 5 on average then you know where you have to tweak the difficulty curve. You could also log the causes of player death and see if something sticks out. You could even publish two versions of the game and see which one generate's longer playtime and thus does a better job at entertaining the players. Social game developers like Zynga use that approach a lot and with great success.
I personally think that's pretty interesting field that I'm definitely going to explore more if I ever manage to complete another game. Even in my last game where I logged only a few things there were a number of valuable lessons to be learned.
For example my stats tell me that Rune Hunt was played 375,267 times with an average playtime of 22:35 (compare that to other versions of your game to see if you improved at keeping the player engaged)
The game has two different endings (after about an hour of gameplay) and I know that both endings are taken equally often (4.5k vs 4k) but that was only after a tweak I made early in development, when I noticed that almost all players experienced the same ending.
The game has 4 levels and the first level was completed 112,000 times, the second 77,000 times and the third only 8,800 times but those that made it through level 3 would almost always finish the game, too. So obviously there's something fundamentally wrong with level 3!
Even if you're developing an offline game nothing would stop you from sending a log-file to your sever for each playthrough.
Once you have the data it's up to your imagination how you'll use it to improve the game. For example do stuff like this:
http://blog.counter-strike.net/science/maps.html