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This wiki page collects fonts which meet two criteria:
1. They are free, in the "libre" rather than "gratis" sense of the word. In the free software world, this distinction is often phrased as "free as in speech" as opposed to "free as in beer." The fonts on this page are all released under licenses compatile with the Debian Free Software Guidelines, which is the usual metric in the free software world. The Open Source Definition is similar, and in the vast majority of cases will cover exactly the same licenses.
Compatible licenses include GPL, OFL, and public domain. Incompatible licenses include most of the Creative Commons licenses (see here for a summary), AFPL, and all "free for noncommercial use" licenses. Perhaps someone will feel moved to create a Good Gratis Fonts page.
2. They are pretty good, by the consensus of the typophile community. There are a lot of really terrible free fonts out there, but relatively few good ones. This is the page for those.
Some time in the mid-90's (todo: get exact date), Artifex Software, the maintainers and commercial licensors of Ghostscript, funded the donation to the GPL world of the URW font set compatible with the standard PostScript 35. These fonts include: Nimbus Roman No. 9 (clone of Times Roman), Nimbus Sans (clone of Helvetica), Nimbus Mono (clone of Courier), Century Schoolbook L (clone of New Century Schoolbook), URW Bookman L (clone of Bookman), Palladio (clone of Palatino), URW Chancery L (clone of Zapf Chancery), Standard Symbols L (clone of Symbol), and Dingbats (clone of Zapf Dingbats).
The Gentium font, designed by Victor Gaultney under the auspices of SIL, is now released under the new OFL font license.
The Doulos SIL font, similar to SIL Doulos, originally an IPA font by SIL International, is now released under the new OFL font license. Wide coverage of Latin and Cyrillic.
The Charis SIL font, similar to Bitsream Charter by Matthew Carter, released under OFL by SIL International is the creator of the font. Wide coverage of Latin and Cyrillic.
JUnicode is another font with a very strong emphasis on Unicode coverage and internationalization. It has essentially complete coverage of the Latin ranges in Unicode, and is thus suitable for Old English, IPA, and other such scripts.
The DejaVu fonts are public domain additions to the Bitstream Vera fonts. Wide coverage of Latin, Greek and Cyrillic.
See the note below.
As used on the Android platform, are licensed under Apache License 2.0. Made by Ascender.
The Computer Modern fonts distributed with TeX are just below the level of quality intended for this page, but have a number of interesting properties and are in fairly wide use for math typesetting. The main font in the family is essentially a clone of Monotype Modern No. 8. Interestingly, these fonts were among the very earliest digital fonts to implement Optical Scaling.
The Utopia license
Luxi, IBM Courier, and Adobe Utopia are widely included in Linux distributions, but the Debian people feel the licenses are not clearly within the DFSG. Utopia was recently re-released by Adobe to the TeX Users Group with a clarified license. The license itself grants TUG the right to freely distribute and modify the font, as well as the right to sublicense the font to other parties. TUG has issued a blanket statement sublicensing the font to any interested parties. It appears that the question regarding the freeness of Utopia has been resolved. This post on Open Source Publishing also comes this conclusion, and includes additional clarifications by Adobe.