But the Danes are rather selective when it comes to the definition of an "island". 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.
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. But if you prefer something a little more cultural, you also will not be disappointed.
An hour's hike from the hamlet of Sandvig, through the hills of Hammeren, brings you to the ruins of Hammerhus Slot, perched on the top of a sea- cliff. While just 5km north of the picturesque town of Gudhjem is the Bornholm's Kunstmuseum, a gallery displaying major works from the Bornholm School that thrived here in the first half of this century.
Gudhjem is also a good jumping-off point for the 6km trip inland to Osterlars, site of the largest and most impressive of the island's fortified churches dating from the 12th and 13th centuries. A similar distance further inland is Almindingen, Bornholm's largest forest, where there's a lookout tower with fabulous views across the island.
If the seven-hour ferry trip from Copenhagen to Bornholm doesn't daunt you, then you may think the one-hour hop onwards to Christianso is nothing.
Christianso served as a naval base in the 17th century, and the stone- lined streets still reflect their military past. These days, the tiny population is made up of artists and fisherfolk (who pride themselves on the delicious spiced herring they produce). If you want to learn more about life on the island, visit the Christianso Museum in the small tower that was once part of a large fort.
For somewhere offering a little more peace and quiet, look no further than the tranquil islands of Lso and Mon.
Little Lso's 114 square kilometres of broad sandy beaches, coastal meadows, heathland and farms cannot satisfy the demands of the average tourist. There are no large hotels with swimming pools and no throbbing nightclubs with neon signs - there aren't even any traffic lights. Other than the straw-thatched maritime museum and the bizarre seaweed-thatched farm museum, there's little else to pull in the crowds. The main attraction is the laid-back attitude of the Lso folk which invariably rubs off on visitors. Ferries from Fredrikshavn on Jutland make the one-and-a-half-hour journey to Lso four times a day.
With Copenhagen just an hour's drive away, if you don't have much time in Denmark but want to experience the country's great outdoors, the undulating island of Mon is probably your best bet.
Despite being connected to the "continent" of Zealand by a pair of relatively new bridges, Mon has retained its rustic, rural feel. Most people come to the island to admire the stunning white cliffs (the only ones in Denmark) and mediaeval churches with outstanding frescoes.
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. As recently as the 1960s, local women still wore the traditional island costume of multiple skirts and a scarf that could be used as a mask against the sand. During the Fannikerdage festival which takes place in early July, you can see these costumes being worn and enjoy local folk music and dancing.
The wild, unkempt but popular Romo is connected to Jutland by a 10km causeway that passes over scenic marshland with hundreds of wading waterbirds dodging between the grazing sheep. The sandy western side attracts an interesting mix of windsurfers, basking seals and nudists.
With all this water, it's hardly surprising that most Danish families seem to own a boat. The protected waters along the south Funen coast make it an ideal spot for weekend yachters. Three popular sailing destinations are Drejo, Skaro and Hjorto, all 10-15km south-west of Svendborg.
At 420 hectares, Drejo is the largest of the three and has a close-knit community of about 100 people and a handful of endangered fire-bellied toads. 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. Tiny Hjorto also attracts lots of birds, but most people come for rest and relaxation. Only 15 people live on the island and there are no cars or motorbikes. 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. All three have camping facilities if you want to stay longer.
Also connected to Svendborg by ferry is ro, the pearl of the South Funen archipelago. Its rolling hills scattered with small villages and thatched farms make it another popular destination among yachters.
One of the best ways to appreciate the island's sights, which include the magnificent moated manor of Sobygard, several ancient passage graves and the historic port of Marstal, is on a bicycle.
If you're feeling energetic you can make it around the island in 7-8 hours. Well-signposted cycle routes help guide the way and ensure you see all the best bits. But if time is limited, take Route 91 which runs along the north coast of the island. Homemade elderflower juice, fresh waffles and other sustenance can be found at the beautiful Gammelgard (Old Farm) along the way.
Bikes can be hired in roskobing, an attractive town of cobbled streets and half-timbered 17th-century buildings that shows few signs of modern times - except during the brilliant July jazz festival. The Danes refer to roskobing as "Eventyrbyen", the fairy-tale town, and few of those who visit it would disagree. The Japanese liked the place so much, they went home and built an exact replica.
denmark fact file
The best way of getting to Denmark is by plane. Scandinavian Airlines (0845 6072772) offers flights to Copenhagen from several UK airports starting at pounds 99 return (with tax extra).
Eurolines (01582 404511) runs coaches between London and several destinations in Denmark three times a week. Tickets cost pounds 97 return but the journey takes about 22 hours.
International Rail Enquiries (0990 848848) provides details on times and cost of trains. Expect to pay around pounds 243 return, depending on the day and time of travel.
Scandinavian Seaways (0171-409 6060) operates ferries between Harwich and Esbjerg (approx. 16 hours), and Newcastle and Esbjerg (approx. 20 hours).
Denmark has an excellent bus and railway network to complement the fleets of ferries scuttling between the islands. With the exception of Bornholm and Christianso (7 hours from Copenhagen), ferries to all the islands mentioned take around an hour or less. Ticket prices are roughly based on journey times and work out at about pounds 5 per hour. Denmark is very bicycle- friendly and you can take your bike over there by plane (as well as by bus and ferry), but check airline first.
Where to stay
Some islands have only a campsite, although most have small hotels and B&Bs. Renting a cottage can work out very cheap. For further information contact the Danish Tourist Board (0171-259 5959), 55 Sloane Street, London SW1X 9SY.