A dialect continuum is a range of dialects spoken across a large geographical area, differing only slightly between areas that are geographically close, and gradually decreasing in mutual intelligibility as the distances become greater. Dialects separated by great geographical distances may not be mutually comprehensible. According to the Ausbausprache - Abstandsprache - Dachsprache paradigm, these dialects can be considered Abstandsprachen (i.e., as stand-alone languages). However, they can be seen as dialects of a single language, provided that a common standard language, through which communication is possible, exists. There are occasions when various nations of the same linguistic origins occupy the same territory and thus speak the same dialect, but have split standard languages located at different parts of the continuum, sometimes causing doubt as to precisely which language is the dialect in question a property. Examples include regions such as Kashmir in which local Muslims declare their language Urdu; Sikhs, Punjabi; and Hindus, Hindi. Similar complications arise across much of the former Yugoslavia whereby Bosniaks, Croats and Serbs may speak the same dialect within the same region, yet all have separate standard languages.
The Germanic languages and dialects of Scandinavia are a classical example of a dialect continuum, from Swedish dialects of Finland, to Swedish, Gutniska, Älvdalsmål, Scanian, Danish, Norwegian (Bokmål and Nynorsk), Faroese, Icelandic, as well as many local dialects of the respective languages. The Continental Scandinavian languages (Swedish, Danish, and Norwegian) are close enough and intelligible enough that some consider them to be dialects of the same language, whereas the Insular ones (Icelandic and Faroese) are unintelligible to the other Scandinavian speakers.
The many dialects making up Dutch, Low German, German and Swiss German are often cited as another canonical example. They form a single dialect continuum, with two recognized literary standards. Although Dutch and Standard German are mutually intelligible only to a certain degree, there are many transitional dialects, for example Limburgish, spoken in parts of the Netherlands and Belgium, and the Low Franconian dialects across the border in Germany.
Although part of the same dialect continuum, the northernmost Low Saxon dialects are in many ways actually farther from High Alemannic/Swiss German than from English. They remain linked by a chain of intermediate dialects, all mutually intelligible to their adjacent dialects, whilst English remains the single West Germanic language detached from the continental continuum: its insular location caused it to develop independently from the continental languages.
Old English was originally a West Germanic dialect, imported from the continent and initially the same language as that then-spoken in what is now the Netherlands, Belgium and Germany from where the new settlers migrated. Initially it remained mutually intelligible with the continental dialects such as Old Saxon, but over time it broke away from the continuum, and today there is no chain of mutually intelligible dialects connecting English to the Continental West Germanic continuum.
Some people believe the Norman Invasion of England and subsequent interference with the English vocabulary is responsible, but it is also to be noted that geographical barriers also, given enough time, tend to cause breaks in a dialect continuum. This suggests that English's location on an island, even if not for French influence, would have still caused it to break away from Continental West Germanic. (cf. Icelandic vs. Continental Scandinavian) The single closest language to English is Frisian, a language split into numerous dialects spoken in the north of the Netherlands and across the border into Germany. It is mutually unintelligible with English however.
Another such network of dialects is the continuum of northern Slavic dialects. These for reasons of tradition are further separated into eastern and western branches: Russian, Belarusian, Carpatho-Rusyn and Ukrainian are recognized as literary standards; all rolling smoothly into Polish, Slovak and Czech, which are in turn closely connected to the Sorbian languages, spoken by the Slavic populations of eastern Germany. Collectively, these dialects form one of two continua. They are geographically separated from the South Slavic dialects by the heavy concentration of the principal non-Slavic populations of Romania, Hungary and Austria.
A separate south Slavic dialect continuum features Slovene and the Serbo-Croatian language; the latter is a network of several major dialects and three literary standards (Bosnian, Croatian and Serbian). These form the western branch of South Slavic dialects which are in turn linked to an eastern branch, comprising Standard Bulgarian and Standard Macedonian which properly form a dialect continuum and share a set of grammatical features that set them apart from all other Slavic languages, with the Bulgarian standard being based on the more eastern dialects, and the Macedonian standard being based on the more western dialects.
The Italo-Western branch of the Romance languages, which comprises Italian, Occitan, Spanish, Catalan, French, Galician, Portuguese, Romansh, Arpitan and Leonese language, as well as other languages with fewer speakers, is sometimes presented as another example, although the major languages in this group have had separate standards for longer than the languages in the continental West Germanic group, and are not commonly classified as dialects of a common language. In recent centuries, the intermediate dialects which existed between the major Romance languages have been moving toward extinction, as their speakers have switched to varieties closer to the more prestigious national standards. This process has been most notable in France, due to the French government's refusal to recognise minority languages, but has occurred to some extent in all Western Romance speaking countries. Language change has also threatened the survival of stateless languages with existing literary standards, such as Occitan and Catalan.
A less arguable example of a dialect continuum within the Italo-Western languages are the Romance languages of Italy. For many decades since its unification, the above attitude of the French government was reflected in Rome by the Italian government which affected the adjoining dialects of this continuum spoken in Northern Italy. These include Venetian and Piedmontese among others. Over the years however, under pressure from the Northern League, the Italian government has yielded in allowing public signs and other media to use both local and national standard dialects in most affected areas.
Turkic languages are best described as a language-dialect continuum. Geographically this continuum starts at the Balkans in the west with Balkan Turkish, includes Turkish in Turkey and Azerbaijan language in Azerbaijan, extends into Iran with Azeri and Khalaj, into Iraq with Turkmen, across Central Asia to include Turkmenistan, Uzbekistan, Kazakhstan, Kyrgyzstan, to southern Regions of Tajikistan and into Afganistan. In the south, this continuum starts in northern Afganistan, northward to the Chuvashia. In the east it extends to the Republic of Tuva, the Xinjiang autonomous region in Western China with the Uyghur language and into Mongolia with Khoton. This entire territory is inhabited by Turkic speaking peoples. There are three varieties of Turkic which are geographically outside this continuum: Chuvash, Yakut and Dolgan. These languages have been geographically separated from the other Turkic languages for extensive period of time and Chuvash language stands out as the most divergent from other Turkic languages. There are also Gagauz speakers in the Moldavia and Urum Speakers in Georgia.
The Turkic language-dialect continuum makes internal genetic classification of the languages problematic. Chuvash and Yakut are generally classified as significantly distinct, while the remaining Turkic languages are quite similar, with a high degree of mutual intelligibility between not only geographically adjacent languages, but also between languages/dialects which may be some distance apart. Structurally the Turkic languages are very close to one another, and share basic features such as SOV word order, vowel harmony, and agglutination.
Arabic is a classic case of diglossia. The standard written language, Modern Standard Arabic, is based on the Classical Arabic of the Qur'an, while the modern vernacular dialects (or languages)—which form a dialect continuum reaching from the Maghreb in North Western Africa through Egypt, Sudan, and the Fertile Crescent to the Arabian Peninsula—have diverged widely from that. Because Arabic is written in an Abjad (a phonetic writing system similar to an alphabet), the difference between the written standard and the vernaculars also becomes apparent in the written language and so children have to be taught Modern Standard Arabic in school in order to be able to write it.
The spoken variants of Chinese are highly divergent, forming a continuum comparable to that of the Romance languages. However, all the variants more or less share a common written language, though there are vernacular variations in vocabulary, grammar, and orthography.
The written language originally shared by all dialects was Classical Chinese, which was in normal use up until the early 20th century. In pre-modern times, Northern Baihua grew up alongside Classical Chinese as a standard vernacular dialect. The modern standard dialect, Putonghua (often called Mandarin), is largely based on Baihua.
Within the dialects, gradations do exist between pure local vernacular and the more refined speech of the better educated that incorporates elements from the standard language or written language.
Of course, the development of the divergent Chinese languages was made much easier because the characters used for writing Chinese are not tied closely to pronunciation as alphabetic or syllabic scripts are. In other words, a Cantonese speaker may write his language much the same as a Mandarin speaker and yet pronounce the written text in an entirely different manner (see Diglossia: Chinese for more information).
The languages spoken in Northern India and Pakistan form a dialect continuum. What is called "Hindi" in India is actually Standardized Hindi, the Sanskrit-ized version of the colloquial "Hindustani" spoken in the Delhi area during the time of the Mughals. However, the term Hindi can be used to enclose all its dialects from east to west—from Bihar to Rajasthan. The Indo-Aryan prakrits also gave rise to languages like Urdu, Gujarati, Bengali, Oriya, Marathi and Punjabi. Of these, Punjabi can probably be included in the northern Indian continuum. Gujarati is also in some ways close to the dialects of Hindi spoken in the southern Rajasthan region.
The Persian language in its various varieties - Persian (Iran), Dari (Afghanistan) and Tajik (Tajikistan and other parts of the former Soviet Union) - is representative of a dialect continuum. Although official and written forms of the language vary less from one another, spoken Tajiki of Uzbekistan would be virtually incomprehensible to a Persian-speaker of the Persian Gulf islands, and vice versa . The divergence of Tajik was accelerated by the shift from the Perso-Arabic alphabet to a Cyrillic one under the Soviets. Western dialects of Persian show greater influence from Arabic and Oghuz Turkic languages, while Dari and Tajiki tend to preserve many classical features in grammar and vocabulary.
Cree is a group of closely related Algonquian languages in Canada, which is distributed from Alberta to Labrador. These languages form the Cree-Montagnais-Naskapi dialect continuum with around 117,410 speakers. These languages can be roughly classified into nine groups. From west to east, they are:
Various Cree languages are used as languages of instruction and taught as subjects, for example, Plains Cree, Eastern Cree, Montagnais, etc. Mutual intelligibility between some dialects can be low. There is no accepted standard Cree dialect.  
Ojibwa is a group of closely related Algonquian languages in Canada, which is distributed from British Columbia to Quebec, and the United States, distributed from Montana to Michigan, with diaspora communities in Kansas and Oklahoma. Together with the Cree, the Ojibwa-Potawatomi-Ottawa dialect continuum forms their own continuum, but with the Oji-Cree language of this continuum joining to the Cree-Montagnais-Naskapi dialect continuum through Swampy Cree. The Ojibwa-Potawatomi-Ottawa dialect continuum have 70,606 speakers. Roughly from northwest to southeast, they are:
Unlike the Cree-Montagnais-Naskapi dialect continuum with distinct n/y/l/r/ð(th) dialect characteristics and noticeable west-east k/č(ch) axis, Ojibwa-Potawatomi-Ottawa dialect continuum instead is marked with vowel syncope along the west-east axis and ∅/n along the north-south axis.