These are links that are not followed by the search engine spiders therefore not indexed by the search engines... I personally think that they are useful because they make the link building process more natural as far as SE are concerned...
"Nofollow" provides a way for webmasters to tell search engines "Don't follow links on this page" or "Don't follow this specific link." Originally, the nofollow attribute appeared in the page-level meta tag, and instructed search engines not to follow (i.e., crawl) any outgoing links on the page. For example: <meta name="robots" content="nofollow" /> Before nofollow was used on individual links, preventing robots from following individual links on a page required a great deal of effort (for example, redirecting the link to a URL blocked in robots.txt). That's why the nofollow attribute value of the rel attribute was created. This gives webmasters more granular control: instead of telling search engines and bots not to follow any links on the page, it lets you easily instruct robots not to crawl a specific link. For example: <a href="signin.php" rel="nofollow">sign in</a>
Nofollow is an attribute for the anchor html tag. It indicates the search engines that the link should not affect the search engine rankings of the target site. It can only drive traffic, but have only a little affect on the website promotion.
No follow links are basically used to let SE bots/spiders not to crawl through some links in your website or web pages. This is to prevent the SE bots from crawling or indexing some pages that you don't intended to, like some unrelated pages or 404 pages.
IMO, nofollow links are still indexed and followed by search engines. However, all nofollow links that Yahoo does follow will not just provide same value compared it to normal link. Same with Google, they also index and follow nofollow links. Though these links don't have page rank value or don't pass PR juice to other page. I don't think nofollow links have no importance on promotions. Any link regardless of having a nofollow value or not can be useful as long as it's placed on a relevant page of a site and the page has some quality content. Hope this helps.
It does and still have use in promoting your site. Putting them in a good content really helps your site, even if not counted as a backlink it can still give great deal of traffic to your site. All links(either dofollow or nofollow) are important in site promotion, it all depends on how efficiently your using it.
Even no-follow gives no seo benefit, it can bring traffic to your site. So its worth to get no-follow backlinks also.