Google Webmasters Tools shows
rel="nofollow" links as a backlink. I believe that
rel="nofollow" helps SEO and PageRank but according to many people it is not. What is your idea about this? Did you see that
rel="nofollow" links also helps your rank and SEO?
rel="nofollow" does not help with SEO. It was created by Google to combat link spam. Links that have that attribute pass no PageRank and do not count as a backlink in any major search engine. Google may acknowledge that it found a link with nofollow but that link will have no value.
How does Google handle nofollowed links?
In general, we don't follow them. This means that Google does not transfer PageRank or anchor text across these links
The nofollow links aren't supposed to be used in the calculation of the PageRank that a page receives. However, people commonly mention that some types of social media nofollow links do pass PageRank. My understanding of this is Google does at least use Twitter links but they aren't using the ones they discover via normal web spidering. Google also receives Twitter data via an API where the links don't carry the nofollow attribute.
However, I don't think the links pass PageRank in the normal way; it has more to do with the way that they rank Twitter reputation. This means that unless you're an authority on Twitter then the links will be meaningless from a ranking perspective. I'm not sure of the details about how authority is calculated but I think it's more than just your number of followers. You can find more about Twitter and how it affects SE Ranking in this Q&A between Danny Sullivan and Google/Bing: http://searchengineland.com/what-social-signals-do-google-bing-really-count-55389
In the past there was also a common SEO technique, called Page Sculpting, where people tried to influence the flow of PageRank through a site by limiting the number of internal links that didn't use nofollow. However, Google modified their algorithm so this stopped working. The nofollow links are now used to calculate the PageRank distribution so more links mean less PageRank per link; even if it's not passed on to all of them.
rel="nofollow" may have a minor SEO role is marking non content, meta, pages as no to be read. For example my login page or my contact form are pages that might not be useful for my site to have in search results and so I can mark the links to them as nofollow, in addition adding meta tags for
noindex or adding to my robots.txt.