The Electronic Entertainment Design and Research (EEDAR) has just released their findings that Xbox 360 games with more achievements generally make more money and sell more copies.
They found "that titles that incorporate online elements into their Accomplishments generate 50% more money than those that do not."
This finding is a bit misleading, however, because not all games have online elements in the first place. It could be that people are more willing to purchase a game if it has an online element.
Furthermore, they claim that "game titles can generate up to 50% more revenue by including Accomplishments with Viral Marketing aspects (User Generated Content, Community or Customization Accomplishments)."
Again, it could just be that these games include this content, which helps drive sales. It isn't necessarily the achievements that are driving higher sales numbers.
Regardless of causality, achievements are definitely awesome and help drive people to play games more than they would without them.