Originally Posted by pseudoswede

Preface: American with only a US passport who doesn't look remotely Swedish

My most common entry into the EU is at ARN. Since Mrs. Swede and kids also have Swedish passports, they dump me and go through the citizen line and grab our checked baggage. When I finally get to a passport booth, the border agent asks for the purpose of my visit as they thumb through my passport. I reply to them in Swedish that I'm here on vacation with my wife and kid(s) to visit my in-laws for a few weeks. The tone changes rather quickly; they then ask a few other high-level questions, compliment me on my Swedish-speaking abilities, and then stamp my passport and wish me a good day.

So yeah, being able to speak the local language helps.

I don't think a border agent at any EU airport has ever spoken to me when exiting the EU. They just simply look for the entry stamp and stamp the exit stamp as close to it as possible.