The peace prize (like the other prizes) is awarded every year in Oslo. The Nobel Prizes were instituted in 1901 when Norway and Sweden were still in a union. The founder, Alfred Nobel, wanted to have one prize given out in Norway, the others in Sweden.
In Norway, the royals only attend the ceremony, and only witnesses it, taking no part in it. The King does not give out the prize like the Swedish King does in Stockholm. This is because the peace prize is so much more political, and the royals are only guests, thus not associated with the prize itself.
After the ceremony there is a grand reception and (black-tie) dinner at a Hotel here in Oslo, hosted by the government, but this is never attended by the royals.
The day after the ceremony, there is a grand concert, which seem to attract more celebrities every year. It has only been a tradition for 10 years I think. Tomorrows concert will be hosetd by Michael Douglas and Catherina Zeta-Jones, that's why they attended the ceremony today. Among those performing are the Cardigans, Craig David and Tim McGraw.
A link to the concert website: http://www.nobel.no/concert/index.html
I believe members of the Norwegian royal family has attended the peace prize ceremony every year since 1906. Usually only the King was present, I think King Olav often went alone, as did probably King Haakon. It is only in later years that more members of the family has attended the ceremony. Crown Prince Haakon (with his then fiancée) and Princess Märtha-Louise first attended in 2000.
The concert was often attended by Queen Sonja during the first years, but later years only the younger royals have been there.