Comparison of Danish, Norwegian and Swedish

Danish, Norwegian (including Bokmål, the most common standard form of written Norwegian, and Nynorsk) and Swedish are all descended from Old Norse, the common ancestor of all North Germanic languages spoken today. Thus, they are closely related, and largely mutually intelligible. The largest differences are found in pronunciation and language-specific vocabulary, which may severely hinder mutual intelligibility in some dialects. All dialects of Danish, Norwegian and Swedish form a dialect continuum within a wider North Germanic dialect continuum.
Mutual intelligibility.
Generally, speakers of the three largest Scandinavian languages (Danish, Norwegian and Swedish) can read and speak each other's languages without great difficulty. This is especially true of Danish and Norwegian. The primary obstacles to mutual comprehension are differences in pronunciation. Because Norway’s largest cities have received TV signals from Sweden’s two national TV channels since the early 1980s, Norwegians generally have a better grasp of Swedish than Swedes do of the Norwegian language because Sweden did not get Norwegian TV until decades later. 
Danish speakers generally do not understand Norwegian as well as the extremely similar written norms would lead one to expect. Many Norwegians – especially in northern and western Norway – also have problems understanding Danish. According to a scientific study, of the three groups, Norwegians generally understand the other languages better than any other group, while Swedes understand the least.
In general, Danish and Norwegian speakers will be able to understand the other's language after only a little instruction or exposure.
History.
In the Kingdom of Denmark–Norway (1536–1814), the official language was Danish. The urban Norwegian upper class spoke Dano-Norwegian, a form of Danish with Norwegian pronunciation and other minor local differences. After the two countries separated, Danish remained the official language of Norway, and remained largely unchanged until language reforms in the early 20th century led to the standardization of forms more similar to the Norwegian urban and rural vernaculars. Since 1929, this written standard has been known as Bokmål. Later attempts to bring it closer to and eventually merge it with the other Norwegian written standard, Nynorsk, constructed on the basis of Norwegian dialects, have failed due to widespread resistance. Instead, the most recent reforms of Bokmål (2005) have included certain Danish-like constructions that had previously been banned.
Writing system.
Generally, Norwegian orthography is more simplified and regularized and closer to actual pronunciation than Danish. As a rule, the graphic differences between the two languages do not reflect actual differences in pronunciation; while there are significant phonetic and phonological differences, they are rarely expressed in writing. The few exceptions are noted below.
Note, however, Norwegian "John, som hadde sett mannen, visste hvordan han så ut" (John, who had seen the man, knew what he looked like), where the dependent clause is parenthetic.
Pronunciation and sound system.
The difference in pronunciation between Norwegian and Danish is much more striking than the difference between Norwegian and Swedish. Although written Norwegian is very similar to Danish, spoken Norwegian more closely resembles Swedish.
Danish pronunciation is typically described as 'softer', which in this case refers mostly to the frequent approximants corresponding to Norwegian and historical plosives in some positions in the word (especially the pronunciation of the letters "b", "d", and "g"), as well as the German-like realisation of r as a uvular or even pharyngeal approximant in Danish as opposed to the Norwegian alveolar trills or uvular trills/fricatives.
Note that in the following comparison of Danish and Norwegian pronunciation, the East Norwegian pronunciation of Oslo is taken as the norm. In practice, most Norwegians will speak a local dialect in most contexts; furthermore, Bokmål itself is not a spoken standard, and is likely to be pronounced with clearly regional features. The most obvious instances are the uvular (rather than alveolar) pronunciation of and the lack of retroflexes in much of Western Norway, and the pronunciation, in some cases, of a retroflex flap instead of in much of Eastern Norway, including the less "refined" forms of the Oslo dialect. All of this is ignored in the following exposition.
Vowels.
Arguably the most acoustically striking differences in vowels are that:
As a whole, Norwegian still preserves the old pairs of short and long vowels, as suggested by the writing system, pretty close to each other, even though the long ones are usually closer. Thus, the grapheme "e" corresponds to long ("sene" , late [plural]) and short ("sende" , to send), while the grapheme "i" corresponds to long ("sine" , his/her/its/their own) and short ("sinne" , anger). In Danish, the tendency of differentiation has led to a qualitative overlapping: also here, "e" can stand for long ("sene" , late [plural]) and for short ("sende" , to send), but "i", besides signifying long ("sine" , his/her/its/their own), has come to correspond to short ("[nogen]sinde" , ever) and, to complicate things further, a short pronunciation is maintained in some cases ("sidste" , last). Most Danish vowels have also many segmentally conditioned allophones, especially more open ones when preceded or followed by .
The following is a table that compares the most common Danish and the Norwegian pronunciations of a letter (without taking into account the grouping of sounds into phonemes, as well as many sub-rules, exceptions and subtleties). Note that in many cases, even when the same IPA transcription is used, the sounds may still be somewhat different in the two languages.
! rowspan=2 | Grapheme
! rowspan=2 | Quantity
! colspan=3 | 
! rowspan=2 | 
! rowspan=2 | 
! /V/
! /rV/
! /Vr/
! rowspan="2" | "a"
! long
! short
! rowspan="3" |"e"
! long
! short
! unstressed
! rowspan="2" |"i"
! long
! short
! rowspan="2" |"o"
! long
! short
! rowspan="2" |"u"
! long
! short
! rowspan="2" |"y"
! long
! short
! rowspan="2" |"æ / ä"
! long
! short