So, I'm currently living in Denmark on the 90 day visa waiver and i would liek to, if possible, stay for the whole summer. I only have about a month left on my visa waiver. One thing I was thinking of doing is that I've heard that France does not stamp US passports as people come in, and I know that Denmark rarely stamps passports if your coming from countries inside the Schengen region. Would it be possible to come intoFrance from a non Schengen country (say England) then go up to Denmark? Is there anyway around this? What happens if you get caught overstaying your visa waiver? I've listened to a lot of hearsay on this subject but would be interested if anyone has any experience with this problem....
Not sure about your specific question, but just to mess things up a bit, some countries - including France - specify that travellers must be able to produce their passports on demand if stopped for any reason (maybe a motoring offence etc.), which kind of negates the whole Schengen agreement.
Worst they can do is send you home I suppose.
The Schengen rule is that you get to stay 90 days out of 180 days in the Schengen states. So going to a non-Schengen state like Switzerland or the UK to renew your visa won't work.
As the conditions for issuing visa's vary slightly from state to state, your best bet is to contact the Danish authorities with your details and ask for ways to extend your stay. If you got proof that you can support yourself (preferably without working anywhere in Denmark), they'll probably say yes. IIRC, by Schengen rules your tourist visa can be extended once to 180 days max.
BTW, I see from your profile that you are an US-citizen. If you have Irish or Bristish ancestors (and you can prove it), you can apply for Irish or British residency/naturalisation in Ireland/the UK. That would give you residency rights within the EU automatically.
Ask the next British or Irish Embassy near you.
I found the information about applying for residence in the UK: