Do "NoFollow" links provide any SEO value?

[applesofgold]

Do "nofollow" links provide any SEO value, particularly for Google? I have heard that they still can, since Google doesn't necessarily follow all of the tags.

Is this true? Is there any value in obtaining nofollow links? Can they also hurt in any way?

Thank you! 
Afshin

Apples of Gold

[MentorMate]

The anchor text adds value, but it is minimal relative to follow links. They don't pass authority however. You need a healthy mix of follow and nofollow links or your link profile will look shady and this could have a negative impact if the search engines think you have an unnatural/spammy link profile.

[applesofgold]

Interesting in terms of having "nofollow" links to promote organic-ness.

[RandyHT]

I am new to this, but I have heard it said that some no follow links likely provide value.  For example, Wikipedia, because it is so well-curated and tolerates zero spam.