We all agree that the letter г in Russian is equivalent to g in English. But why is the letter г in some Russian words pronounced [v]?
For example:
сегодня = pronounced as if it is written: севодня
ничего = pronounced as if it is written: ничево
его (for example: его семья) = pronounced as if it is written: ево
Льва Толстого = Lva Tolstova
хорошого дня = haroshovo dnya
для того что = dela tovo chto
The Russian orthography is based on morphological-historical principles, which means it tries to write morphemes the same way all the time and keep the historical spellings of those morphemes (the latter is the main feature of the English spelling, too).
This г read as в is an example of historical spelling. It's only found in the genitive case of masculine and neuter gender forms of
The point is that all the rest of the Slavic languages have a [g]-type sound in those forms; it's only in Russian that [g] changed to [v] in the genitive case endings. Still, the Russian orthography preserves the traditional spelling with г. Perhaps the reason for this is that in the Moscow dialect, which was later taken as the basis for Standard Russian, [g] changed to [v] no earlier than in the 17th century, i.e. quite recently. The reason the change occurred is the fact that bisyllabic unstressed endings tend to weaken: [оgо] > [оо] > [оvо] — first [g] dropped out and then the epenthetic [w] > [v] appeared. This trend originated in the Northern Russian dialects and can also be traced in some Pomeranian Lechitic dialects.
As for the word сегодня, in which the г read as в, it's in the middle of the word and not in the ending, and that is also a trick of orthography. Cегодня is an adverb which is actually a frozen noun phrase сего дня "[on] this day", in which both words are in the genitive case, сего being the genitive case singular masculine form of the archaic demonstrative pronoun сей "this" which is no longer in use. It was replaced by этот. Writing adverbs that appeared from free phrases as a single word without spaces or hyphens is typical of Russian: вперёд (forward) < в перёд (to front), завтра (tomorrow) < за утро (after morning), etc. As you can see, even with сегодня, it's in the genitive case ending that г is read as в.
Also note that when I say "ending", that means a grammatical ending, not just the last sounds of the word. In Russian, there are some words that end in /evo/, but nevertheless are spelled with в because that /evo/ is not a genitive ending, for example марево ['ma.rʲɪ.və] "haze, mirage". In this word the root is марев- and -o is the nominative case singular neuter ending. Once in a Latvian newspaper in Russian, I saw an ad that started with ДЁШЕГО! which means "Cheap!" and is pronounced ['dʲo.ʂɪ.və]. That is really a funny mistake since the word is actually spelled дёшево because it isn't in the genitive case. The root of the word is дёшев- and -o is the suffix that turns adjectives into adverbs. Remember, not every Russian word that ends in [və] is written with г.
With animate nouns, the accusative case coincides with the genitive case, so everything which was said above about the genitive case is valid for the accusative case animate as well.
Historical phonetics, I guess. In some southern dialects of Modern Russian, the letter Г г is still pronounced as [ɣ] almost in any position (as in modern Ukrainian). For some times, the Russian koine was a mix of competing dialects without a unified standard.
That trend resulted in an interesting competition between the phonemes [g] and [h/ɣ] in the times of Derzhavin and Lomonosov. Namely, in words for 'spiritual' and 'high' lexis (such as Бoг, ангелы, богатство and господа) the trend was to pronounce the letter Г г as [h/γ], the former variety matching the intervocalic position. The unified modern way to pronounce Бoг as [boχ] is a relic of that time.
That trend led Trediakovsky to posit two different letters for two distinct sounds.
For details, see the humorous poem by Lomonosov from that time (in modern orthography).
Later, the intervocalic [ɣ] developed into [v] (as was the case with some Frankish loanwords into French, where intervocalic [ɣ] became [w] or [v].)
Basically, in addition to сегодня, any combination of -ого and -его for a genitive masculine/neuter singular is pronounced as [-óva /-ava] or [-éva/-iva] respectively, whether with a stressed vowel or not, and the only exception I can think of now are words of the много [mnóga]-type.
Сначала звук "г" стал произноситься фрикативно, как он сейчас произносится в украинском языке и часто в южнорусских говорах (Украина и соседние регионы, например Белгородская область). Так, например, Брежнев произносил "г" фрикативно, потому что он был из Днепропетровской области.
Потом в -ого- мягкое "г" вообще перестало произноситься. "Красного"->"красного" с мягким "г" -> "красноо".
Потом между двумя буквами "о" стали добавлять "в".
Первые слова с таким "в" употребляются в 14 веке. Сначала это произошло в Ростово-Суздальской земле, потом такое произношение проникло в Москву и стало восприниматься как правильное столичное произношение, а тогда уже распространилось повсюду.
