Polyglotism is the ability to speak several languages with a high degree of proficiency. There is no consensus on exactly how many languages a person has to speak to be a polyglot. One could say "four or more", since speakers of two or three languages are commonly called bilingual and trilingual, respectively. The term multilingual is similar.
Linguist Richard Hudson uses the term "hyperpolyglot" for a person who can speak six or more languages fluently.
There are several theories as to why some people learn many languages with relative ease, while others struggle learning even one foreign language. One theory is that a spike in testosterone levels while in the uterus can increase brain asymmetry.
Others have suggested that becoming a polyglot has nothing to do with such factors and is actually just about hard work, which any adult can apply despite not being naturally talented. 
The neuroscientist Katrin Amunts studied the brain of Emil Krebs and determined that the area of Krebs' brain responsible for language—Broca's area—was organized differently than in monolinguals.
Notable living polyglots
Notable dead reputed polyglots
It's generally impossible to prove the language abilities of dead people, and the claims are not backed up with reliable evidence of how the claims were confirmed. In fact, the claims often don't even mention which hundred languages the person supposedly spoke, how well they spoke them, or how they learned them (without the internet or modern dictionaries, and in a time of much less travel and cosmopolitanism).
With that said, the following are people whose names are associated with claims of massive multilingualism:
- John Bowring (1792–1872), an English political economist and the 4th Governor of Hong Kong. He could speak 100 languages.
- Dr Abdul Rahman Ghassemlou (1930–1989), an Iranian political activist and polyglot who could speak 10 different languages fluently. He mastered 11 languages including his mothertongue.  
- Hans Conon von der Gabelentz (1807–1874), a German linguistic researcher who worked on more than 80 languages.
- Utpal Dutt (1929–1993), an Indian actor, director, and writer-playwright and author. He could speak 8 languages.
- Friedrich Engels (1820–1895), a German-English industrialist, social scientist, and father of Marxist theory alongside Karl Marx. He mastered over 20 languages.
- Nicolae Iorga (1871–1940), a Romanian historian, politician, literary critic, memoirist, poet, and playwright. He could speak Aromanian, Romanian, French, Italian, Latin, and Greek fluently at the age of fifteen.
- Emil Krebs (1867–1930), a German polyglot and sinologist. He mastered 68 languages in speech and writing and studied 120 other languages.
- Uku Masing (1909–1985), an Estonian linguist, theologian, ethnologist, and poet. He was claimed to know approximately 65 languages, and could translate 20.
- Giuseppe Caspar Mezzofanti (1774–1849), an Italian Cardinal. He supposedly spoke 39 languages fluently.
- John Milton (1608–1674), an English poet famous for his epic Paradise Lost. Milton could speak English, Latin, French, German, Greek, Hebrew, Italian, Spanish, Aramaic, and Syriac. He was also proficient in Old English. He coined 630 terms in the English language.
- Mario Pei (1901–1978), an Italian-American linguist and writer. He was claimed to be fluent in at least 38 languages and acquainted with the structure of more than 100.
- P. V. Narasimha Rao (1921–2004), Indian lawyer, politician, and activist who served as the ninth Prime Minister of India (1991–1996). In addition to eight Indian languages (Telugu, Hindi, Urdu, Oriya, Marathi, Bengali, Gujarati, Tamil), he spoke English, French, Arabic, Spanish, German, Greek, Latin and Persian.
- Dr José Rizal (1861–1896), a Filipino national hero, optometrist, artist, author, and scientist who could speak 22 languages.
- R.M.P. Sosrokartono (1877–1918), a translator and war correspondent for the The New York Herald Tribune. He was claimed to speak 34 languages (24 non-Indonesian languages, 10 local Indonesian languages).
- Heinrich Schliemann (1820-1890), a German archaeologist who excavated Troy and Mycenaean civilizations, could speak German, English, French, Dutch, Italian, Portugese, Spanish, Polish, Swedish, Greek, Latin, Russian, Arabic, and Turkish.
- Nikola Tesla (1856–1943), a Serbian-American inventor, physicist, mechanical engineer, and electrical engineer. He could speak Serbian, Czech, English, French, German, Hungarian, Italian, and Latin.
- Noah Webster (1758–1843), a lexicographer, English spelling reformer, and author. He mastered 23 languages.
- Harold Williams (1876–1928), a New Zealand journalist and linguist. He was claimed to speak more than 58 languages.
- Babel No More: The Search for the World’s Most Extraordinary Language Learners. By Michael Erard. Free Press; 306 pages. ISBN 978-1-4516-2825-8