One difference between the USA and many European countries is that Americans are not issued "ID cards". French citizens, for example, are issued a "carte d'identité" and are supposed to have it on them. I have been stopped by police in both France and Spain and was asked to see my ID card. The most recent time was about 5 or 6 years ago when I was touring in Spain. I was suddenly surrounded by 3 plainclothes officers in who demanded to see my "tarjeta". I told them I was a tourist and I handed them my passport. They looked for the stamp of my entry into the EU (which was at a German airport) and phoned someone who verified that my passport stamp and I were legitimate. They were polite but were incredulous that I had biked all the way from Bilbao to Santander the previous day. I had a somewhat similar experience in Paris many years ago. My understanding is that it's perfectly legal in those 2 countries to be stopped without cause by the authorities and be required to show your ID card (or passport), unlike the US.
About 10 years ago while driving north to Tucson from the Mexican border, I was stopped at a roadside checkpoint. I honestly don't recall what I was asked, but I wasn't asked for any documentation. The entire exchange lasted a few seconds.
I've seen the videos of people being stopped in more recent years with the whole "Am I being retained?" scenario. One thing which both civil libertarians on the political left, and tea party types on the political right generally agree upon, is that these stops are unconstitutional. I believe that "stop and frisk" is similarly unconstitutional. Indeed, I would say it is obviously unconstitutional.
It's true that at borders and ports of entry, we all have far fewer rights. The only border where I've been hassled is the Canadian border (and I've been to at least 3 dozen countries and on every continent except Antarctica). Twice at land borders entering Canada, I was told to go inside to be interrogated. The Canadian border agent many years ago was very polite and her questions were reasonable. The more recent time was highly annoying and I later filed a formal complaint with the Canada Border Services Agency because of the behavior of the border official. I eventually received the expected bureaucratic reply because I suspect the border official in question lied when asked about my allegations about his behavior. I later learned that it is shockingly common for both Canadian and American citizens to be on the receiving end of abusive and unprofessional behavior from border officials of their neighboring country. BTW, the Canadian border official looked at every file on my old netbook and every digital photo in my camera. My understanding is that they have the right to do that, and that was not what I complained about. FWIW, I toured in a couple of communist countries and was treated far more politely at the border than I was that time (about 3 years ago) at the Canadian border.