As a Dane i often argue with my Norvegian girlfriend about where most vikings lived: In Denmark or in Norway? I always think of Denmark as a easier place to live and trade because its closer to the more populated areas of central Europe.
The viking population of Norway at the height of the viking age (around 800 AD) was probably around 80,000 people, by the end of the viking age ca. 1050 it is estimated to have been around 200,000 people. I don't have a specific source for these numbers right now, I heard it at a talk by Jón Viðar Sigurðsson in Reykjavík I know he has a couple of books on Norwegian history that likely has more information.
As for Denmark (that is the modern territory of Denmark) it was significantly higher, at the turn of the 8th century the population was around 500,000 reaching the million mark around the 13th century.
Source for Norway: Norsk historie 800–1300: frå høvdingmakt til konge (not sure if its avaliable in English)
Edit: The Danish numbers were provided to me by this website http://natmus.dk/historisk-viden/danmark/oldtid-indtil-aar-1050/vikingetiden-800-1050/magt-og-aristokrati/hvor-stort-var-danmark-i-vikingetiden/ I intended to call them, but they seem to be closed on Sundays.
During the Viking age, out of the modern Scandinavian nations, Denmark had the highest population. The highest density region is a bit harder to answer because it depends on how big you want your regions to be. An island like Bornholm or Gotland would probably have the highest population density, but an island like Björkö or the north shore of the Viksfjord or the modern Schleswig region are pretty densely settled too.
The best way to know this is to simply look at the amount of settlements that have been found from this period. While you can never come to a completely accurate answer on this basis, because you do not know what percentage of the settlements of the past have been preserved (and found) to our times, it does give you a good idea of the relative population density between regions. Both Denmark and Norway have a good archaeological research density (meaning that they both have been comparatively well researched), and in both regions, areas that were suitable for settlement back then are still settled today. We have plenty of continuity in place-names in both regions as well, so that gives us another good tool for estimating the amount of settlements. In Denmark, settlement is fairly well spread out throughout the country, with no clear empty zones. Settlement does concentrate in the coastal area, particularly around the Belt and the islands, with the western and inland area of Jutland as well as the centre of Sjælland being less intensely settled. In Norway there are clear gaps (just like today) because only a small part of the country is actually suitable for agriculture. We can also see this more sparse settlement in the pollen record (preserved plant seeds) that suggest that Norway was more forested than Denmark (which was almost treeless). In Sweden, or central and eastern Germany, the wild inhospitable forests still separated small pockets of human settlement, but in Denmark, all land was contiguously cultivated and in use. In Norway, the mountain landscape was similarly 'utland' separating cultivated areas. It is only in the later Viking age (and the early Middle Ages) that these outland is claimed for settlement, leading to a great many new settlement names from this period and often containing 'clearing' or 'new settlement' in the placename (places ending on '-thorp' or '-røde'), also in Denmark where the heathlands and grazing areas, and the aristocratically owned forests, were now more intensely used.
In the more narrow sense of the word 'viking', as in 'where did most of the 8th-to-11th-century pirates come from', I would have no idea how to answer that. It is possible that population pressures were higher in Norway because it was harder to expand settlement into the utland as was going on in Denmark and Sweden during the Viking age (leading to a predominantly Norwegian Norse settlement of the North Atlantic and areas overseas), but it is also possible that the absolute lower number of Norwegians means that they were numerically still drowned out by the masses of Danes, Gotlanders, Svear, Angles, Wends, and other Baltic peoples.
Denmark, southern Sweden(Skåne) and the Mälardalen area has been the most populous areas of Scandinavia since prehistoric times, both the earliest approximations and the amount of archeologic remains points to this.
At the end of the Viking age Norway is supposed to have housed around 27 000 households, which means something around 185 000 people more or less. Sweden and Denmark would have had a population around 400 000 in the 10th century.
EDIT: There have been much better answers posted, and I will add that I didn't find a very good source on Denmark, and other people here have put Denmark at around 500 000 in the 9th century. Edit 2: All my numbers are present border approximations.
It is of course impossible to know for sure if different parts was more prone to going a viking than others. It's been noted that most historical sources wasn't able to discern between the different norse peoples, I don't remember where I've read this, but there are instances where the christian scribe wrote that "danes" was visiting/raiding but the archeological records have shown that they where most probably norwegians.
Sources:
The Cambridge History of Scandinavia. 1st ed.