Despite being connected to the "continent" of Zealand by a pair of relatively new bridges, Mon has retained its rustic, rural feel.
Lying 200km east of Copenhagen, beautiful Bornholm is the archetypal holiday island destination.
If you like to bask on a beach, head for Dueodde in the south where there's nothing but superb sands and a string of campsites.
As Alan Havsteen-Mikkelsen, who grew up on the pastoral island of Bornholm, told me: "We don't really think of Funen and Zealand as islands.
They're more like continents." And indeed they are, at least when compared with the country's other 404 amazing microscopic microcosms.
Another great holiday destination are the windswept islands of Fano and Romo, off the coast of south-west Jutland.
Fano, 15 minutes by ferry from Esbjerg, is long, flat and dominated by heathland, dunes and sandy beaches.Despite the great fire of 1942 which destroyed a cluster of 17 old farmhouses, Drejo still has numerous attractive period buildings, including an interesting church that dates from 1535.Skaro, population 25, is shaped something like a rabbit's head and, rather fittingly, part of the island's salt-meadows are a wildlife sanctuary, given over mainly to 50 species of breeding birds.The only thing you might feel obliged to do is to walk around the island but that takes only a couple of hours.If you don't have your own yacht, it is possible to visit these islands on a day trip via the small ferries from Svendborg.Ferries from Fredrikshavn on Jutland make the one-and-a-half-hour journey to Lso four times a day.