Some countries have such checks. Does Germany also check the criminal records of immigrants?
Unlike the US, Canada or Australia, I don't think Germany generally requires applicants to submit extracts from their criminal records to apply for a long-term visa or residence permit. I don't know about each and every country but I think it's very common in the Americas, not so much in continental Europe. Belgium does however require such a document, covering the five years immediately preceding the application.
A criminal conviction does not automatically make a person ineligible for a short-stay Schengen visa either and applicants are not routinely asked to disclose it. But visas and/or entry can always be denied on “public security” grounds, i.e. if there are reasons to think you intend to commit other crimes and present a current danger.
I would suspect that an outstanding warrant (including a European arrest warrant) could get you arrested at the border, though. Consulates and border guards definitely have to look for a potential ban in the SIS, at least for non-EU citizens.