Hi Mark,
I've had to do a lot of backlink analysis and removal before so this is my view.
If the directory lists links in an unnatural looking manner (i.e. just a long list with little text about the link), I would remove it. Some directories have managed to avoid any algorithm updates for now but I'm sure they will eventually get hit.
The volume of link removal you do will really depend on how large your back link profile is. I had to work through about 20,000 links which needed to be removed as they were from low quality article sites and directories. We received the unnatural link warning in GWMT and filed a re-inclusion request. This got turned down and so we had to dig even deeper into the links pointing to our site.
Just be consious of how many 'good' links you do have. If you go straight into removing a lot of directory links and leave yourself with very few 'good' links to your site, it could be an issue for you. It's really your call.
Personally, I'd remove them if the directory looks poor, has no social media presence and looks spammy.