Times (New Roman)
Arial
Comic Sans
Papyrus
Copperplate Gothic
Hobo
Cooper Black
Eurostile
Courier New
Brush Script/Mistral

I think you have a problem because during that time there is a big change in technology to the personal computer from the typewriter. Then you need to ask whether you are talking about personal and business correspondence, the screen, or print, or signage. Also Europe and the US are somewhat different.

Used in the last 50 years or designed within the last 50 years?

Maybe the point of the exercise is in fact to establish these 'types' of changes as mentioned by William, best bet is to choose a theme (i.e. typewriter to computer) and go from there, of course with good reasoning clear in your mind.

I like your idea of "famous fonts".

By focusing on fonts that were honored and acclaimed (rather than just being used a lot), it narrows the field to fonts that were well-respected and discussed, and which had something of a story and aesthetic theory attached to them, and whose designers may even have been known by name, in the professional fields of graphic design and typography.

It also means fonts that were used by typographers and designers to create layouts, not merely being used by readers (end-users).

You may have to say something about fame vs. notoriety.
Certain typefaces which were much discussed were more vilified than respected, e.g. Souvenir, ITC Garamond, Comic Sans and Papyrus.

Certainly Helvetica and Univers were central to design theory, as practised and taught in the late 20th century.
And Futura (although designed in the 1920s).

That raises a good benchmark: did a typeface have a book written about it, or its designer?
(Renner, by Christopher Burke, centres on Futura).

Some of the best-known typefaces were well-known because their foundries were great publicists, or because their designers were well-known.

For instance, in the 1990s, Emigre magazine, published by Emigre foundry, was the focus of an intellectual movement, in which faces like Barry Deck's Template and Zuzana Lickpo's Matrix became iconic. Dead History was also quite famous, theoretically, although little used.

Neville Brody's Industria was symbolic, in many ways, of design in the 1980s and 1990s, first as the face of the influential magazine he art directed (The Face), then as one of the most-used early DTP faces. "The Graphic Language of Neville Brody" was a best-selling graphic design book, further cementing the fame of Industria and its designer.

Similarly, Avant Garde was famous because of the iconic (that word again), eponymous magazine, and its much-awarded designer, Herb Lubalin.

And Meta, by Erik Spiekermann, perhaps owes something of its fame (quite apart from its popularity in use) to its designer's career and celebrity as a graphic designer, author, conference speaker, and founder of FontShop.

As there is no way to verify exactly the 10 (or 20, or 100) most used fonts, it's safer to say "10 of the most important and used fonts for this period". Trying to keep an eye in printed materials also from '60s, '70s and '80s, I think the list is:

Times New Roman
Helvetica (Arial as a variant introduced with Windows dissemination)
Courier New
Palatino
Bookman
Souvenir
Futura
Frutiger
Copperplate Gothic
Garamond (in its many variations of weight and style)

Other relevant ones: Century Schoolbook, Century OldStyle, Sabon, Commercial Script, Minion, Avant Garde, Brush Script, Caslon, Eras, Bembo, Gill Sans and Univers.

(My perception is based on Latin America, US and UK printed materials.)

and Bodoni, Zapf Chancery, Verdana, Georgia, Baskerville…

It's hard to ignore any default Microsoft or web fonts.

I don't include fonts which popularity was built basically during years 2000–2010 because this is relatively small considering the whole period. So, Georgia and Verdana are out, IMHO.

Georgia and Verdana are landmark typefaces, IMHO. These were a concerted effort to address mostly screen use, the Web, and across the board interoperability. Something out of the Emigre fold is also landmark. Add to that Garamond, Caslon, Bodoni, and Baskerville, which were all quite a bit older but workhorse types used for quite a bit. Bodoni more for display than text. I would also add OCR, Times and Futura

@dezcom: OCR-A or B?

In that vein, MICR might be worth considering.

While I do not know off the top of my head, the first family to include both a serif and a sans might make the list as well. Rotis springs to mind.

...the first family to include both a serif and a sans.

Clearface, 1908.

When talking about Garamond, Caslon, Bodoni and Baskerville, it is important to state which version one is speaking of, as there are many of each. None of them is really "a typeface" in the singular sense.

T

None of those faces, even in revival, are 20th century designs.
That would be like calling a Mozart symphony a 20th century work, because it was performed in the 20th century on 20th century instruments.

My only criteria to build the list above was font usage during last 50 years, regardless its time origin. About font developed during the last 50 years, I mostly agree with Nick Shinn –except about Meta because its diacritics are badly positioned and its all caps does not works so well.