From my experience, BingBot does follow links despite them having a nofollow attribute. I can see it currently in our logs: thousands of requests per day for pages that are linked using nofollow hyperlinks. I did check the IPs as well as user-agent and they seem to be legit requests from bingbot.
Whether or not Bing then uses this for anything (indexing, ranking...) I don't know, but I can confirm it does follow the links.
As per other search engines, I don't have a blanket answer to cover all, but I can say I'm only seeing this from by Bing and (to a smaller extent) Yandex. The rest don't seem to be following the links, although not to an extent that makes me notice it.