I prefer the Royal Guards in Copenhagen when looking at them against other regiments around Europe. They go about their business, marching to and from the Amalienborg Palace through the streets on a regular, if not daily basis.
They always have a police escort, generally one police officer on foot whoi sometimes struggles to control the public when the Guards halt at traffic lights and road junctions.
Copenhagen is a Royal City, so expect to see some of the Royal trimmings when you visit here - like guardsmen marching through the streets, either to or from their city barracks. Even on rainy days. No umbrellas for these hardy guys!
(I was watching them from inside MJ Coffee on Gothersgade.)
Every day at noon you can watch the changing of the guards in the court-yard of the Amalienborg Palace. When the Queen is at home you can see the flag with her colours and her royal coat of arms.
The Guard start at Rosenborg Palace at 11:30 and they marche along Gothersgade, Noerrevold, Fredriksborg, Koepmagergade, Oestergade, Kongens Nytorv, Bredgade, Sankt Annae Plads and Amaliegade to Amalienborg Palace, where the actual changing of the guard takes place at 12:00 sharp.
At the Amalianborg Slot you can witness the changing of the guards every day at noon. It's really a great sight to see. The funny thing is though, that when I was there the guards changed as well, but it was past 2 already.
They are a lot more friendly than the Londoners! These almost look embarrassed as they walk outside Amalienborg Palace. There is a changing of the guards at 12.00 so you see these lads parading down from Rosenborg Castle half an hour before, the band playing their flutes and brass. In fact, they are so punctual I can set my watch accordingly and know lunch is near when I hear them outside the office :-)