Why is personal information (DOB, marital status) listed on CVs in Europe and can it be omitted?

Marital status is completely irrelevant: leave it out. Discrimination based on "Oh, I think you're about to have kids and take a bunch of maternity leave" is illegal.

In practice, date of birth can be inferred from the dates at which you got your degrees and what jobs you've had. OK, you might be a prodigy who got their BA at 14 and their PhD at 17, but the overwhelming majority of people aren't. Or you might be a total bum who was unemployed until the age of 40 and then got a BA at 43 and a PhD at 48 but, again, the overwhelming majority of people aren't that, either. So including your date of birth doesn't really say anything that the recruiter couldn't guess.

Age discrimination is illegal in the UK, and I'd assumed it would be EU-wide. The usual form would be to require somebody to be within so many years of their PhD, though even that's not-really-so-indirect age discrimination.

I suppose items such as marital status, children, professions of parents, place of birth, etc., are not so much there for providing any information as such, but rather form a part of what "belongs" to a complete CV.

You can leave some of them away, but skipping too many of them (without filling your CV in another way) may send a signal like "This person has never bothered to learn what a 'properly done' CV should look like. They are uneducated and/or not diligent about what they do."

Now, this is based upon what I learned back in school, may be country-dependent (I'm in Germany), and - at least here - should probably rather apply to small companies (whose HR people might rather expect adherence to traditional form than the most modern trends in recruitment processes when evaluating CVs) than to academic departments.

Despite differences in the different EU member states, there were attempts to create a kind of EU standard for CVs. This is called "Europass" and was created together with social partners and national training authorities. According to their website the main scope is:

• Ηelp citizens communicate their skills and qualifications effectively when looking for a job or training.
• Ηelp employers understand the skills and qualifications of the workforce.
• Ηelp education and training authorities define and communicate the content of curricula.

While there might be differences in different industries, in my experience it serves well as a guideline in academia (since you ask on academia SE, I assume this might be your main interest). According to their examples (1, 2) it is perfectly fine to keep personal information like date of birth and sex (and/or gender) out of your CV. Discrimination by age, race and sex/gender is not allowed in the application process. Especially public institutions, such as universities and research institutes have strict rules against discrimination. You shouldn't face any disadvantages by not stating personal information, such as DOB, number of children (...). Besides in most cases it's clearly irrelevant.

Both a friend of mine and I applied in academia in a EU country which wasn't our homecountry relying on the Europass guidelines and both of us got hired. So those guidelines don't appear to be frowned upon.

However: Some years ago it was at least in Germany considered as a standard to include personal information (as already mentioned in another answer*). I think especially people working as a professor for a couple of years simply haven't adapted their CVs to today's standards.

Good luck!

*) On a side note: In school I was thaught, that information, which can give hints on your personality must be included in every case. Especially profession of parents, siblings, age, hobbies. Apparently this was supposed to help HR to find the most fitting person for the job and the company. This was outdated at the time I was at school (and sometimes even considered unprofessional, as I was told during an internship to which I applied using those guidelines), but the curriculum hadn't been updated.