I can't give you any quantifiable data I'm afraid but all I can say is that "they work" from my experience - both for the local map/carousel listing and for the normal vertical search.
One thing that I have seen is that they are more successful when you a) make every citation exactly the same (address, number etc) and b) when you include those details on your website, preferably sitewide in a footer or header.
It's pretty much Google's way of seeing if you're a local authority - looks for your address and phone on your site, looks for that same stuff on places on yelp, yell, qype etc. The more of those citations you have, the better really.
I've yet to see citations like that have a negative effect, providing all of the sites are reputable and legit. That's why I'm slightly hesitant about some of those local/business specific directories - are some of those really "authority" websites? But for citations, it's all good and you don't really have anything to lose.
Plus you throw in the fact that some people do start their searches on some of those sites, particularly yelp, and all of a sudden having a listing there is a decent traffic channel itself. I've seen a few sites where some of the top referrers are these citation sites.
Just make sure you really are who and where you say you are. If it's virtual offices/VOIP phone numbers, you're gonna have a bad time. Wouldn't surprise me if Google can already detect these automatically.
Would make for a good case study if done en masse for sure.