I've had a '360 for over a year now and I can honestly say that when the Achievement notification pops up, it rarely distracts me.

I actually think that Achievements have opened up a different avenue of gaming for me. Like you I play a game to experience the game, but where before I would have likely have stopped playing the game on completion, I'll now go back and try and work out how to gain some of those extra Achievements.

This has opened up avenues of the game that I'd have not explored before or forced me to learn a new move, skill or way of doing something.

So I'm actually getting far more use out of the games than I would of, however I draw the line at doing something I don't enjoy for the sake of unlocking an Achievement.

For example, with the multiplayer gaming I won't go on and play against Billy Random just to unlock an Achievement. I only play against people I know in the real world or who are friends of friends, which makes it a far richer experience for me.

I think that the achievements can also motivate. If your in a slow or tough part of a game, gaining some points can be enough to spur you onwards. Or if a friend unlocks a tough achievement the competitive instinct in me will often try and match them.

I guess at the end of the day, Achievements are just a modern interpretation of the Arcade scoreboard.