nofollow links contribute towards keyword relevance through the anchor text and that's why they appear to help, but the law of diminishing returns applies to nofollow because of this. There's only so much relevancy you can get for a keyword.
If you have very high relevancy to a keyword and weaker backlinks vs a competitor who has very strong, authoritative backlinks but weaker relevancy to the keyword then you'll beat him for that keyword.
dofollow links contribute towards both keyword relevance through anchor text as well as providing 'strength', 'link-juice' which is a variety of things ranging from trust rank, authority, pr etc.
That's all you need to know about dofollow vs nofollow and knowing this you'll understand why people still find nofollow links useful and why they only find about 10-15 of them useful. Simple.