Bag and Baggage had this question.
Short answer: Nothing whatsoever. The word "blog" doesn't appear in any European legislation yet, so general copyright rules apply.
So what would the general rules mean for blogs? I have a few observations.
1. Employer Ownership
For authorship of computer programs, the 1991 directive on the legal protection of computer programs says in Article 2
"3. Where a computer program is created by an employee in the execution of his duties or following the instructions given by his employer, the employer exclusively shall be entitled to exercise all economic rights in the program so created, unless otherwise provided by contract."
For all other works the default depends on the Member State. In Germany, the employee owns the content by default. In contrast, the United Kingdom has the default the other way around.
Any default can be changed by contract. If the employee is hired for creating works, it is probably a good idea to address the question of ownership in blog content in such a contract. On the other hand, most blog content doesn't have any economic value, so the question of copyright ownership might not be ever so important.
2. General Copyright
If there is no employer to consider, general rules on copyright apply.
If blog content is protected by copyright at all, that copyright is owned by the blog author.
I think that in many blogs (this one included) many entries don't qualify for copyright in the first place. If all I do is link to some other blogger's post or to some newspaper article, there doesn't seem to be much of any creative activity involved. That's more a vote than a work.
If someone would object to that view and say: "Any simple link in a blog entry is protected by copyright", that would prevent other bloggers from also linking to the same URL without asking the author of the first link. That doesn't make much sense.
However, if someone takes an RSS-feed of a blog that contains only links (like the great "Current Copyright Readings" by M. Claire Stewart) and publishes it in a way that removes the author's name, that might be illegal under the 1996 database directive.
A few weeks ago German blawg authors found their RSS-feeds without attribution in the homepage of a German lawyer who probably hadn't given much consideration to the copyright situation, and definitely hadn't bothered to ask any of us. See this post in my German blog.
Most authors objected, and a few days later the RSS-feed mirroring was replaced by simple links to the original blogs.
From the database directive, Article 2:
"2. For the purposes of this Directive, 'database` shall mean a collection of independent works, data or other materials arranged in a systematic or methodical way and individually accessible by electronic or other means."
So even if the individual blog entry is only a link and doesn't qualify for copyright protection, there is protection as "data or other materials arranged in a systematic or methodical way and individually accessible".