I think you all already know where I stand on Achievement systems.
...yeah, I'm a little fond of them.
Others have already mentioned the good aspects of achievement systems, so I don't need to elaborate on them much further. They only
add to your game, and the only thing of note they've ever removed was cheat codes (and even those have been steadily eroded away through the rise of DLC). I like seeing a game reward me, however little, for doing something outside the realm of normal gameplay activity. Some of my most memorable gaming moments have been in the course of chasing trophies, which have often showed me whole new ways to play the games I enjoy.
Some games, most notably Final Fantasy XIII, have even rewarded me for my excellence with unlockable XMB Themes (Fang from FF XIII was my reward for a hard-earned Platinum trophy, and I've had it as my XMB Theme ever since as a testament to dedication). Others, like Xenoblade on the Wii, give you in-game rewards like XP bonuses for earning achievements, and that's great as well. They're simply a great way to entice players to really delve into a game's mechanics and secrets, and I enjoy using the trophy system to see how far along my online friends are with games I'm also playing. It's fun, costs developers very little time or resources to implement, and if you don't want to take part in the hunt you don't
have to.