high_jinx - you mentioned the old school concepts that I grew up on. No save games (unless the game happened to give you a code that spit you back out at a certain location), leaving the NES on for days. Back then, we had high scores. All games had either a scoring mechanism, or a progress mechanism (which boss did you get to, what level is your hero, etc.).
Games are not always so specific, and not all friends like playing the same games. I look at achievements, well GamerScore specifically, as the new version of the arcade high score. Even if you and your friends play different games, you can brag about certain achievements, or your overall gamerscore. Sure, some games are easy to get 1000, some are nearly impossible... but unless you've both only played 2-3 games, it starts to average out.
It's a testament to geekdom!
