Ordered by how well the claim holds, not by the size of the number.
Documented
Kató Lomb
Hungary · 1909–2003 · around 16 languages
Interpreter and translator, and the most useful of the lot because she wrote down her method instead of being mysterious about it. She learned largely by reading novels she barely understood and pushing through, and insisted she had no special gift. Her line worth keeping: language learning is the one thing worth doing badly.
Documented
Richard Simcott
United Kingdom · living · 16 fluent, many more studied
One of the few whose ability is on video in most of the languages he claims, which is a low bar that surprisingly few clear. He has studied more than fifty at some point and is careful about the difference between studied and speaks.
Documented
Lýdia Machová
Slovakia · living · 9 learned, 7 maintained
Learned all of them without living abroad, which quietly dismantles the most common excuse. Adds roughly one every two years and is explicit that maintenance, not acquisition, is the real cost.
Documented
Alexander Arguelles
United States · living · reads around three dozen
Notable for refusing to give a hard number, which is itself the mark of someone counting honestly. Attributes it to thousands of logged hours rather than talent, and keeps the log.
Reported, unverified
Emil Krebs
Germany · 1867–1930 · 68 claimed
A diplomat who reportedly worked in 68 languages and studied over a hundred more, often learning one through another rather than through German. His brain was preserved after death and studied for structural differences. The figure comes from his own era and was never tested by anyone applying a standard.
Reported, unverified
Giuseppe Mezzofanti
Italy · 1774–1849 · up to 100 claimed
A cardinal credited with as many as a hundred, though roughly half of those were dialects of languages already on the list. Michael Erard went to Bologna to examine the archive for his book on the subject and came back unable to settle it either way.
Did not hold up
Ziad Fazah
Lebanon · living · 59 claimed
Listed by Guinness until 1998 as speaking 58 languages. On live Chilean television he was asked basic questions by native speakers in several of them and could not answer. He may well have known them once and lost them, which is a real phenomenon, but the claim as stated did not survive the test.
The pattern is hard to miss. The people whose numbers hold up are the ones who quote the smallest figures and describe their method in the most detail. Everyone claiming a number above forty is being counted by somebody else.