The nofollow tag is important to those responsible for search engine optimization as it enables them to indicate to search engines not to count links with the nofollow tag as votes in its favor, controlling their reputation along the way.
Using the nofollow can help SEOs and webmasters in general avoid problems with search engines believing they are selling influence or are somehow involved in schemes known widely as generally unacceptable SEO practices. What that means is that the right time to use nofollow is primarily on paid links, but many have found them useful on comments, user-generated content, even embeds all types. Essentially it can be used any time you don't want your site to be seen as endorsing a link to another site (the target site).
Google's Gary Illyes posted a tweet recently confirming that it does make sense to use nofollow, particularly when you're writing about a bad site. Illyes also suggested in the Twitter conversation resulting from the post that the nofollow tag may not be necessary in every instance - calling it "silly" for reputable news publications to use the tag on all their external links.
While it doesn't make sense to blanket no-follow every link away from your site, feel confident that there is value in doing so selectively because your reputation may be on the line.
