Backlinks are of two types - No-follow and do-follow
Nofollow : Backlinks that do not pass any backlinking credit. You can use nofollow attribute with backlinks which you don't trust.
But they may, nevertheless, bring streams of targeted traffic
By using dofollow links, the site will help increase PR and nofollow links are useless, But nofollow links could bring you some traffic. You should always mixed with link building Do follow Keep Going No-follow. Because some search engines are counting No-Follow the links too. Each tweeter response with Yahoo answer both gives are no-follow.
I searched for it, Nofollow are not crawling a link by search engine. Do-follow allow search engine to crawl links. No-follow tag we can use if we are using a link for reference not for crawl. Both are good for traffic.
A nofollow link is a link that is included on a webpage using standard html markup but includes an attribute to prevent passing link juice or reputation to the destination page. This type of link does not improve the link target search engine ranking.
Whenever you put the rel=”nofollow” attribute in the link that time it’s tell the search engine they cannot follow the destination inside the link it means it does not transfer the page that the link is pointing. This link called as a Nofollow link.
For Example: <a href="http://www.joomlateachings.com/" rel="nofollow" >Tutorial Joomla</a>
You should have a blend of nofollow and dofollow backlinks. The highest PR backlinks you are likely to find are often nofollow, they may (or may not) be useful as a backlink but they do add authority to your site which will in turn help your ranking. My site is PR4 and 50% of my links are nofollow.
If you will get any no-follow link that will help to generate traffic but don't help to get any link juice. But no-follow link concept is useful sometimes, if you give any link from your site to other sites then you can put a no-follow tag in their link and they can't get any link value from your site.
Nofollow attribute developed by Google in 2005 for the reason of increasing spamming on blogs and other sites.
If a site has NOfollow attribute on their external links, Google will not pass any kind of values to money site, I'm not sure about links from Wikipedia may be Google pass their reputation to other resources those are linked with them.