Origins
The word 'snake' descends from Old English 'snaca' (snake, serpent, crawler), from Proto-Germanic *snakō, from PIE *sneg- (to crawl, to creep). The etymology is transparently descriptive: a snake is 'the thing that crawls.' This naming strategy — identifying a snake by its limbless locomotion — is one of the most widespread in the world's languages.
The PIE root *sneg- (to crawl) also produced 'snail' (Old English 'snæġl,' the small crawler) and is likely related to 'sneak' (Middle English 'sniken,' to creep along), giving English a family of words united by the concept of low, furtive, legless motion. The sn- consonant cluster in English carries strong associations with the nose and with low, sliding movement: 'snout,' 'snore,' 'sniff,' 'snot,' 'sneak,' 'snail,' 'snake.' Linguists debate whether this is a true phonestheme — a sound cluster that carries inherent meaning — or merely a statistical coincidence.
The Proto-Germanic cognates are consistent: Old Norse 'snákr' (snake), Swedish dialectal 'snok' (grass snake), and German 'Schnake' (which shifted meaning to denote a crane fly or large mosquito-like insect rather than a reptile). The semantic shift in German is notable — the 'crawling thing' was transferred from a reptile to an insect, while the primary German word for snake became 'Schlange' (from 'schlingen,' to wind, to twist).
Proto-Indo-European Roots
English possesses an unusually rich vocabulary for this animal. 'Snake' is the native Germanic word. 'Serpent' entered from Old French 'serpent,' from Latin 'serpēns' (present participle of 'serpere,' to creep, to crawl — from PIE *serp-, to crawl). 'Adder' is also Germanic, from Old English 'næddre' (snake, serpent), where the initial 'n-' was lost through misdivision of 'a naddre' into 'an addre' — one of the most famous examples of false splitting in English. 'Viper' comes from Latin 'vīpera,' a contraction of *vīvipera (live-bearing), because vipers give birth to live young rather than laying eggs.
The cultural associations of snakes in Indo-European mythology are overwhelmingly negative, from the serpent in the Garden of Eden to the Norse world-serpent Jörmungandr. Yet the medical symbol of the caduceus (two snakes around a staff) and the Rod of Asclepius (a single snake) associate snakes with healing — likely because the shedding of skin symbolized renewal and regeneration. The Greek word 'pharmakon' (drug, medicine, poison) captures this duality: the snake's venom could kill or cure.
The Old English word 'wyrm' (worm, serpent, dragon) was once used interchangeably with 'snaca' for snakes and serpentine creatures. In Beowulf, the dragon is a 'wyrm.' The modern English restriction of 'worm' to invertebrate annelids is a later narrowing of meaning.