I'm surprised no one mentioned Wing Commander, that game had a great achievement system. The reason it's so great is because no one perceived them as "achievements" in today's sense. Wing Commander kept track of your performance and depending on how you played you could receive medals. This worked because it was perfectly integrated into the game's universe, you were serving in the army and when you were about to receive a medal you got invited into your superior's office, he had a short talk with you and then you were given the medal during a ceremony. The "achievements" enhanced the atmosphere of the game, in fact it would feel off if they were missing. To look up your medals you didn't go into some menu, you clicked on your locker and then you saw your uniform with your medals on it and your rank was written below.
The achievement systems today do the opposite, they don't fit into the world at all, it's just some popup that pulls you out of your immersion and reminds you that you are playing just a video game. These achievements ruin the experience and I turn them off whenever I can.
Personally, I find that achievements do more harm than good. Aside fom the aforementioned immersion breaks the obsession with protecting these worthless systems leads to more DRM, no cheat codes and savegame encryption. Back in the day the achievement was beating the game, then beating it on a higher difficulty or beating it with certain limits, like no reloads, no kills or no power ups. Most games today just don't have anything to offer in that regard, you play once through them to you see the story and then you sell it at eBay, GameStop, Amazon Marketplace or whatever. Achievements are just a means to stretch game by wasting the player's time with riddiculous things like "do this thing this many times". It's nothing new though, games have always been padded with some useless BS like pointless fetch quests or just some stuff randomly scattered throughout the world for the player to find.
Honestly, I wouldn't care if all that was just some optional nonesense I could just turn off, then I'd let the losers* brag about the ePenises as if those mattered, but more often then not the developers will force you to go through the tedium. Can you believe I still haven't beaten Metroid Prime, just because someone thought it would be a good idea to send the player on a wild scaveger hunt all across the planet before allowing them to enter the are of the final boss? In Super Mario Wii I was able to use a cheat code (I have hacked my Wii), so I don't have to collect those big coins, because you need all the big coins, of which there are three in each level, from each world to unlock levels in world 9. I'm not going to waste my time with that, there is no challenge in it, its' just a waste of time.
_____________________________________
* just to clarify this, I'm not calling people who are good at video games losers, I mean those people who will just mindlessly grind away their time with something that has no challenge in it just to get some useless shiny sticker which is worth nothing.