Depends. If it just some site that annoyingly demands an account in order to upvote or comment on something, and it makes sense for my fb account (which doesn’t have my real name or birthdate or much real info) to be doing that, and it offers an easy login via facebook, and I don’t think it’s going to spam me or anything, then I’ll use fb to login to be able to comment etc. If not, then generally not.
That is, I think, “Is this site going to do something annoying with my fb ID?” and “Do I care if this site gets my fb id?” and “Does it make sense to do what I want to do on this site as my db persona (mostly a political rant account with some interesting stuff and friended to some of my friends and family)?” and “Would it be better to use my actual name or ID on this site?” or “Would it be better to use another or a new ID for this site?” Based on my reaction to those sorts of questions, I do or don’t.
Oh, the above is my behavior in my usual mode using computers. On mobile I’m different – I often don’t use fb at all on mobile devices, because they tend not to be hooked up to my facebook ID for various reasons of annoyance with fb mobile apps that has me not install them and not associate the devices with my facebook id.