Useful for giving your backlinks some diversity, many would say good for SERPs but I don't agree, you'd need hundreds of thousands of nofollow links to rank a decent keyword. Concentrate on looking for high PR dofollow links without too many OBL (outbound links) and it will pay off. Also reply with something related to the topic or you'll risk it getting removed.
The correct term is "nofollow". nofollow backlinks are useful in that they give you link diversity. If all your backlinks are dofollow, then that might look a little suspicious by the search engines as it wouldn't be very natural.
I do agree and that is the fact about "nofollow" attribute. Search engines don't avoid them and it might be wary if you get all the links from "dofollow" attribute.
In case nofollow back links are more on your site rather than do follow links, it will be very difficult for the site to rank. So concentrate on high pr sites with do followlinks.
nofollow link will not give you backlinks... But these backlink can generate referral traffic for your website. As far as their indexing is concerned, Google does not index nofollow links but if other links on those web pages are dofollow your backlinks will get crawled.
"nofollow" link is not read by Google and such Search engine. there are few search engine which are neglegible reads nofollow links. So it is only usefull if the visitor of the site where you had taken "nofollow link" clicks on your link, then visit of your site will be increase. But if he click on the link and close your site within 30 second the it will go to bounce, means fake click. So better is not take this type of link
It's still good to have a nofollow links as you can use it as a referral link. From experience I use this so my competition will have hard times looking for those quality links when they try to reverse engineer my backlinks.