A couple of years ago i would have answered 100% yes, but now my feelings about my country are more diverse - there's lots of things that i'm proud of, like our social security system ensuring that ppl don't have to live in the streets like in so many other countries, our attitudes towards e.g. gay and lesbians allowing them to marry n adopt (don't ever come to Denmark Asp, it might be contageous

), our great (and free!) educational system, our readiness to help other countries etc. etc.
But there's also plenty of things that i'm not proud of, like the way refugees and asylum seekers are treated, if they eventually manage to enter the country (we have very strict laws in that area), or the 2 stupid idiot newspaper editors who decided to publish the drawings of Muhammed, or my government's decision to join the US n UK in the war in Iraq although most of the Danish population were against etc.
But overall i still think Denmark is one of the best countries to live in in the world (unless your a refugee or asylum seeker), so yeah i'd have to say that i'm proud of my country.