I think it's important to distinguish the EU and Denmark a bit to understand the situation. Denmark do not use the Euro, but have locked our currency to the Euro, like Switzerland had. Right now speculators are trying to pressure the Danish krone and see if we'll buckle like Switzerland did, but all indications seems we won't and have a very different setup than Switzerland did (public national bank and a long history of having the krone locked to the Euro (D-mark before that) vs Switzerlands private and short history of ditto). That is why our national bank issues negative interest rates, to make it less appealing to buy kroners and drive the price up.
What it means for investors is morgages are really really low interests here. They are closing various morgage bond products right now, because they are not allowed to issue then with negative interest rates. We're currently looking at converting (again) from a 3% 30 year morgage to a 2% 30 year loan, but maybe we'll even see a 1,5% 30 year loan soon, if this keeps up.
Along side really cheap morgage loans, I still see our global investments go up, so far so good.
So if you're interested in buying a property here, now is a good time to get a really cheap morgage, if you're interested in that.