Do nofollow backlinks pass pagerank?

Interesting question,

I would have said 100% no, the whole purpose of nofollow was to prevent page rank being passed to a target site and saying you cannot vouch for this site. 

However lately google have expanded the rel tag to include sponsored (rel="sponsored") and user-generated rel="ugc"). This leads me to wonder if in some cases the nofollow tag may carry some weight some in time in the future.

However, Google have not confirmed this. They are just saying it will give them a better understanding of links and spot unnatural link patterns. 

Personally, I would have liked to see them add a rel="resource" to indicate the link is to a page where you resourced your content, something like wiki do on their pages. I guess though this tag would be misused and the spammers would abuse it. 

As Chedders and KnowOneSpecial mentioned, this has changed recently.

This is a bigger deal than it is being given credit for.

The advice has always been if a nofollow link is useful go for it! They can bring traffic that is valuable too. My personal take is that they will be treated as a regular link from sites that are considered high enough authority and are trusted (perhaps only a certain distance from a trusted seed set of sites, or more likely meeting certain algorithmic conditions).

Many nofollow links will continue to have almost no SEO value, its just not guaranteed that it will have no effect.

Consider sites with a high percentage of nofollow links and they could actually see a positive or negative impact from this change.