I've been reading a lot of Orderic Vitalis's "Ecclesiastical History" lately, and he suggests that whilst Danish kings and nobles may have been Christians from the time of Harald Bluetooth in the mid-10th century, Christianisation didn't properly get underway until the reign of King Cnut IV (reigned 1075 - 1086). For example, he claims that the Danish armies that invaded England under Sweyn Forkbeard and his son Cnut from 991 - 1016 and under Sweyn II in aid of the Yorkshire rebels against William the Conqueror in 1069 were mostly pagan, and that English Christianity went into almost terminal decline during the period of Danish rule over all England (1016 - 1042). Obviously Orderic has his problems as a source - firstly, he wants to give as favourable a portrayal of the Anglo-Saxons as possible and secondly, as a cultured half-Englishman half-Norman living in Northern France, one of the great epicentres of 11th and 12th century cultural and intellectual dynamism and religious reform along, it would have been easy for him to look at Denmark as a peripheral barely civilised backwater. Still, I've heard that Christianisation took a long time in many places (i.e. pagan burial rituals continuing to be practiced in rural Lithuania centuries after the conversion of Grand Duke Jogaila in 1386) and some historians and sociologists have argued that Northern Europe was not truly Christianised until the Reformation (Jean Delumeau) or indeed never at all (Rodney Stark).
It depends on the region; The Jelling Stone in Denmark announcing the establishment of Christianity as the religion by Harald was still significant even if it didn't mean the whole country was converted yet. As did the Icelandic þing decision of 1000 and Saint Olaf's supposed completion of christening of Norway a few decades later. The Swedes were supposedly still largely pagan according to Adam of Bremen in his own day (1070s) and the last concrete mention of pagan resistance there would be the martyring of Saint Botvid by a pagan in 1120. Adam of Bremen also claims fringe areas of Denmark - Bornholm and Blekinge as not having been converted properly until their bishop missioned there in the 1060s. However, Adam has a bias in wanting to hold forth the importance and relevance of the missionary work done in the ecclesiastical province of Hamburg-Bremen that he represented and there's a commonly-held interpretation that he neglected or minimized the contributions made by Anglo-Saxon and Irish missionaries. Adam was not a first-hand witness to conditions in Scandinavia either (and Orderic even less so).
Archaeology actually pushes the dates back a bit. Christian burials first turn up in Bornholm already in the late 900s. The excavation of Kata Farm and other sites in Sweden now show that at least the elites in Götaland were converting in that same late-900s time frame as the core areas of Denmark, and the same goes for Østfold and Rogaland in Norway. Whereas areas like Trøndelag, Agder, northern Norway and the inner parts of eastern Norway converted later, as did Svealand in Sweden. Evidence shows rapid changes towards Christian burial practices in the 11th century in Norway. Even in Sveland's Uppland, historians tend to side with an earlier date than a later one; it was probably mostly Christian by the 1080s. Adam's claim that Emund the Old (circa 1050s) neglected Christianity could be interpreted as Adam's judgement on Emund's tolerance of paganism. It's been suggested the traditional date of 1120 for Botvid's martyring may be a bit late too.
Of course by Christian burial practices we primarily mean east-west oriented graves and the abandoning of cremation. Needless to say, that doesn't necessarily mean the buried were completely Christian. (Burials in churchyards was also a thing that would come later) But Scandinavia was likely almost completely converted by 1100, and in that century Christian institutions were strengthened considerably and what holdouts may have existed would have the thumb-screws tightened by the fact that things like inheritance rights became contingent on conversion. Although law codes we have from the 13th century, like Gulathingsloven, ban pagan activities, there's no concrete evidence of such activities still happening in that period. (one might compare to Magnus Erikssons Country Law of 1340 which finally banned thralldom in Sweden but entered into force something like 70 years after the last mention of anyone owning a thrall)
As I said in a post yesterday, the nationalists/romantics of the 19th century really wanted to believe paganism had survived longer than it actually likely did, because they'd adopted the view that pre-Christian beliefs were a core part of national identity. (and that crowd is still around although not so represented in academia anymore) But we don't know that any actual Viking Age Scandinavians felt that way. If it was such a core part of their identity, one would perhaps expect more resistance than we know of. On the contrary, it's been argued (e.g. in Skiftet) that resistance to conversion may have been primarily rooted in opposition to the associated political and social changes, not the faith itself.
The Baltic States and Finland were converted later (and the Scandinavians played no small part in those Baltic Crusades), and those were much more isolated parts of Europe. Scandinavia had frequent cultural contacts with the continental and southern Europe for a millennium before the Viking Age ended. As for Delumeau, his ideas that most European weren't 'really' Christians (not just the north) doesn't have that much support. Although it's based in the correct observation that the average masses did not view nor practice Christianity the same way as the priests and educated classes, judging that this means that these people weren't Christian is anachronistic because it's based on later standards. These people regarded themselves as good Christians and by the standards of their time, were. It (and associated "two-tier" models like Muchembled's) have also been criticized since the start for being overly simplistic and creating a false dichotomy because there was in fact significant interplay between the 'low' and 'high' religious traditions. E.g. the medieval canonization of saints was often little more than an official sanction of a popular veneration that'd started spontaneously.
Anyway, Denmark was mainly Christian well before Canute IV, in fact most of Scandinavia probably was by that point. Anyway, this is a pretty brief post, but to mention some sources and further reading:
Nora Berend (ed), Christianization and the Rise of Christian Monarchy: Scandinavia, Central Europe and Rus' c. 900–1200, Cambridge University Press, 2007
Anders Winroth, The conversion of Scandinavia: Vikings, merchants, and missionaries in the remaking of Northern Europe, Yale University Press, 2014
Sten Tesch (ed), Skiftet - Vikingatida sed och Kristen tro, Artos & Norma, 2017