rainborick - 3:30 pm on Aug 31, 2013 (gmt 0)
I think Planet13's post puts it well, although for completeness I would include the original purpose of rel="nofollow": user generated links, as outlined in the January 2005 post announcing Google's support. I think it's important to remember that all of the major search engines soon joined in supporting it, and they all continue to support it to this day.
Using links as a ranking factor predates Google, it's just that Google's method of differentiating the value of individual links (ie. "PageRank") was a game-changer. After that, all of the search engines refined their use of links, but links are still a universal ranking factor. And that's why they all have always had guidelines prohibiting artificial links, and why they all support rel="nofollow".
If you accept that reducing the impact of artificial links improves the quality of search results everywhere, then it is worthwhile for Google and the other search engines to try to discover those links and sometimes adjust the rankings of websites that employ them in violation of their guidelines. Then, too, it is also beneficial to users to give webmasters a simple tool that allows them to have paid ads, user-generated content, and other features on their websites without risking their rankings or negatively impacting the SERPs.