Kongernes Nordsjælland, or in English - the Kings' North Zealand, is a national park in Nordsjælland, Denmark. The National Park status has yet to take full effect, due to disagreements on the parks boundaries, but the necessary law passed through parliament in 2008, and protection will be effective from some time in 2010 or 2011.
A large portion of the national park is taken up by Gribskov, Denmark's 4th largest forest, covering some 5600 hectares (ca 14.000 acres), the landscape here is undulating with varied vegetation, but mostly pine, beech and some majestic old oak trees. The forest is bordered by Esrum Sø to the east, Denmark's 3rd largest lake by area, and largest by water volume, at the southern corner is a protected bay rich on birds, further east through an area of farms and fields lies the shallow, 2 km2Gurre Sø surrounded by relatively untouched forest. South of Gribskov is the expansive deer park Store Dyrehave where the star shaped trail system used for the royal Par force hunts still dominates. To the north you will find Tisvilde Hegn and Arresø.
While not exactly rich on fauna by most standards, for a densely populated area like Denmark - and Sjælland in particular, the range of animals to be spotted here is richer than almost everywhere else in the country outside the Wadden Sea. Mammals living in the park includes many species of deer (red-, roe-, fallow- and sika deer) which constituted a large part of the royal interests in the northern forests. You can also see foxes as well as the European Badger, and if you are extremely lucky you can sometimes spot Osprey or the White-tailed Eagles, but more common sightings up in the air includes the Common Buzzard and to some extent the Honey Buzzard and Sparrowhawk.
There are no fees to enter the park, and the only fee you are likely to encounter is the compulsory angling license  if you plan on fishing in any of the lakes; 35 Kr/day, 100 Kr/week or 140 Kr/year.
Gribskovbanen (The Grib Forest railway) is one of the oldest private railways in the country. It was built between 1880 and 1924, mainly to haul timber between Gribskov and Copenhagen, which was a tedious venture to do over land, but it has also carried passengers nearly since its beginnings. Today it mainly carries commuters to Hillerød where passengers can continue with the S-train to and from Copenhagen, but during the summer its also packed with vacationers going to their holiday homes or the beaches on the North Coast, or on small treks in Gribskov (stops: Gribsø, Kagerup & Mårum).
Since you're in Denmark, naturally another way of getting around would be on a bike, from Hillerød two marked bicycle routes takes you towards the North Coast. Route 32 towards Helsinge and Tisvildeleje (Tisvilde Hegn) takes you along the western boundary of Gribskov, and route 33 takes you directly through Gribskov to Gilleleje. Besides those two bicycle routes there are ample of paths through the forests, and scenic thinly trafficked roads to take you throughout the park.
While the royal connotations in the parks name mainly refers to the 3 grand royal palaces of Northern Zealand; Kronborg in Elsinore, Fredensborg Slot in Fredensborg and Frederiksborg Slot in Hillerød, these are actually located inside the respective cities, and are as such not part of the national park itself - although they are perfectly feasible to visit as part of an excursion to the park. There are however, also a number of ruins related to the royal history of the lands contained in the park, that relates to the kings of old, though you'd probably need an interest in archaeology or history to go out of your way to see these sites.
Asserbo Slotsruin, Bisp Absalonsvej 31 (nearest address). Erected as a monastery by Absalon, the founder of Copenhagen, in the 11th century for the Carthusian Order, it was since converted to a palace, taken over by the king, and abandoned after a fire. Archaeological excavations have since exposed the foundations and remaining parts of the walls, and the old moat also remains. Nearby is another excavation of an abandoned village and a number of tumuli inside the forest(56.024054,12.052488)edit
Dronningholm Slotsruin, Auderødvej 40 (nearest address). A castle ruin. Originally build by King Valdemar II (1170-1241) for his wife Dagmar in the 12th century. It was since passed on to Seignory, and eventually to decay. Many of building materials was used to reconstruct a local mill after a fire, and so only the foundations remains, but there is nice views over the lake.(55.9702501,12.0568541)edit
Gurre Slotsruin, Gurrevej 425 (nearest address). Arguably the most impressive of the parks ruins, its origins are hazy, but it gained prominence under King Valdemar IV (Valdemar Atterdag), who also expanded the castle significantly in 14th century. According the legend he became so attached to it that he "would give up his place in heaven to keep it", something not lost on various Danish poets throughout the ages. The only real visible part remaining is the bast of the main tower, which still rises up to 3 metres above the foundations.(56.019517,12.5051599)edit
Søborg Slotsruin, Bygaden 58, Gilleleje (nearest address). An important locality from the viking age and up to its days as a royal castle from the 12th to the mid 16th century when it was disbanded following the Count's Feud civil war. Many of the stones were used during the construction of Kronborg castle in Elsinore. The moat and ground layout of the old castle is still visible(56.090714,12.31005)edit
Esrum Canal is a 9 km canal between Esrum Sø lake and the north coast at Dronningmølle, build in 1805 to transport timber from the forests to Copenhagen. The canal lost its importance when the railway was build, and was subsequently abandoned. However, it is still visible in the landscape, and while partly overgrown, parts still carry water and many of the old installations related to the canal is still there. The trail where horses used to haul the barges along the canal still exists, and offers a fantastic walk.
Fruebjerg. is a historic 65 metre hill-top in the middle of the forest, which towers (well at least for Denmark) above the surrounding areas and offers some nice views over Northern Sjælland. The site was home of the massive fruebjergmødere gatherings at the turn of the 19th century, closely related to Grundtvigs folk high school movement. A tradition that has recently been revived.(55.97587,12.28176)edit
Troldeskoven is a special area of Tisvilde Hegn where 100-200 years old weather worn Scots Pines with twisted and crooked branches create a peculiar atmosphere, which has prompted locals to dub the area the - enchanted or troll - forest. The phonemon is caused by strong winds and poor soil conditions.
Esrum Monastery, Klostergade 11, Esrum (North of Esrum lake), ☎ ''+45'' 48 36 04 00 (email@example.com), . 11am-4pm (only Th-Su in the winter). This used to be the biggest monastery in Scandinavia. Only a few buildings remain. Shops, restaurent, and many activities for children.Free, but DKK for some exhibitions. edit
Æbelholt Kloster museum (Æbelholt Abbey Museum), Æbeltholt 4, ☎ +45 4824 3448. May - Oct: 11 - 16 (Monday closed).. The ruins of the largest medieval Augustinian abbey in the Nordic countries. The small museum on the grounds, has exhibitions about the medical history of the Augustinian order, including a garden with medical herbs, and some 300 skeletons on display. Once every year there is a middle ages themed market day held, at the grounds around mid June.(55.9447708,12.2119859)edit
In Nyrup Hegn and Klosteris Hegn there is free camping which is rare in Denmark.
Dronningholm (Arresø), (Shortly after you pass the castle ruins there is a small parking lot on the right, the grounds are 200 metres on the south side of the small lake), ☎ +45 47 72 30 01, . A campground for up to 10 people near the Dronningholm castle ruins near Arresø lake.(55.969937451,12.063482893)edit
Nordhuse (Arresø), (Follow Nordhusvej around 900 metres and turn left down a small unnamed road - look for a yellow marker - from the parking lot its 300 metres ahead.), ☎ +45 47 72 30 01, . a small campground right by Arresø lake.(55.989285406,12.081068185)edit
Hvidkilde (Gribskov), (From Kagerup station follow Hærvejen around 1 km east, and turn left on Hvidkildevej, it will be on your left after crossing the train tracks.), ☎ +45 32 50 00 17, . a campground in an abandoned gravel pit, close to a small spring of the same name.(56.007119258,12.292821837)edit
Ornedvej (Gribskov), (From the bridge at Orned plantation where biking route 32 passes the Pøleåen stream, continue 300 metres to the east), ☎ +45 32 50 00 17. A small campground in a beech forest.(55.986207425,12.265125108)edit
Nødebo Holt (Gribskov), (From Nødebo village down the Holtevej road to the lake), ☎ +45 32 50 00 17. Close to the southern end of Esrum sø (lake). Views over the bird reserve, bathing in the lake is possible, and there are tables, benches and a barbecue/campfire. (55.970930207,12.359803945)edit
Endrup Hegn, (Follow Davidsvænge road to the forest, once there, follow the left path for around 400 metres, the site will be on your left), ☎ +45 48 48 21 00. Two shelters in a small forest area near a small village near Fredensborg. around 3 km from the castle, with room for 5 in each shelter.(55.993160101,12.421039762)edit
Ravnebakken (Krogenberg Hegn), (Follow the Ravnebakkevej road to the old ranger house called Ravnebakkehus, and turn up the small path opposite). Shelter in the eastern part of the Krogenberg Hegn area, well protected from the wind, around 10 sleeping places.(56.014349899,12.509653533)edit
Edens Have (Hellebæk), (From the parking lot at Skindersøvej follow the gravel road around 150 metres). Really good shelter for up 20 people just around a km from the beach with electricity and toilet facilities, but it requires reservation.(56.068134540,12.528271693)edit