Is there an option or plugin to give users the choice to show their blogs to everybody or only to registered users? 

Private blogs with a list of users who have access are not an option.

Any thoughts about this? 

At the moment there is only a general setting to show blogs to groups of users (guests, users, admin) but I would like to have a user setting to give them the choice to choose between public (also for guests and search engines) or only for users who have logged in.

Thanks,
Markus

At the group level, you can allow members in a group to create private blogs. When creating a private blog, you choose explicitly which other members can see your blog (in addition to permitted moderators).

It is not possible out of the box for a user to create a blog and choose whether only logged in users can read it or not, however.

Thank you for the explanations. 

I would like to suggest this feature/setting for a future release. It was available in vBulletin (migrated from there to here) and some users need/want this privacy level.

Or is there a plugin/add-on for this? - I haven't found one yet. 

To look for an existing plugin check out our marketplace, and to suggest a feature for a future version please post in our feedback forum.