hey erik,
referring to an answer from mark at a similar question it looks as there is no export tool in easyblog right now:

Unfortunately we don't have an export tool yet currently but you could always migrate them from the database layer itself. For instance, you could export the tables with a prefix of jos_easyblog_* through PHPMyAdmin and re-import them again on your new database 

so as mark described you could do this with the database, another idea would be (if the other services support it) to simply import the easyblog posts via rss.
hope that helps

I could do that.

The problem is that I'm thinking about closing down the blogging function on my site and I want the users to be able to export their blogs.

Maybe there is some plugin that could work for this. I guess I have to search and see if I can find something.

Thanks for sharing Alex