If you see a row of eight accented characters on the left that resemble the ones on the right (not necessarily the same font), then you have a Unicode polytonic Greek font installed and your browser should be ready to go:

ἀέῃϊὸῥϋᾧ       characters

If not, or if you want to try something new, here are samples and links to a number of fonts.  And that number is much larger than when I first posted this list!  My font, Aristarcoj, is now available in version 2, which has been updated to include new characters in the Unicode standard.

The Aristarcoj characters embody my personal appearance preferences.*  My other pick as to appearance is GentiumAlt (the regular Gentium uses the tilde accent), but unfortunately it still contains no numerals.  I also wish it had a “handwritten” theta.  Alkaios also has some features that I like.

Why is it called “Aristarcoj”?  Because it appears as the name of the Greek mathematician Aristarchus when displayed in its own characters, such as in a drop-down menu.  :)  The standard non-Unicode characters are mapped like the WinGreek fonts, making them mutually compatible.  It contains no Latin charater set, nor any other language (except Coptic, which coexists in the standard Greek Unicode range), and is thus a small file, unlike the big Unicode fonts which tend to be half a megabyte or more.

The fonts below are all freely downloadable.  More commercial and shareware fonts are available, but my goal is to help make Unicode Greek freely accessible.  I have not included several fonts which seem to have some problems or are not intended for general use, such as Arial Unicode MS.  DISCLAIMER:  I make no claims as to the functioning of any of the fonts or software below.  I have tested Aristarcoj with Windows 98, 2000, and XP using four different browsers, and have suffered no untoward effects.  Please use customary discretion when downloading any software.

These fonts contain all of the Greek and Coptic characters, including archaic numerals such as digamma:
Aristarcoj My font, Aristarcoj version 2;
download it here
Arev Sans Arev Sans by
Tavmjong Bah
AttikaU AttikaU by
the American Philological Association
BosporosU BosporosU by
the American Philological Association
Cardo Cardo by
David J. Perry
CMU Serif CMU Serif (and 32 others in the family!) at
Computer Modern Unicode fonts
Works in Word and Firefox, but not IE6 on my computer.
Hindsight Unicode Hindsight Unicode by
Darren Rigby
KadmosU KadmosU by
the American Philological Association
These as well contain all the numerals:
DejaVu Serif DejaVu Serif from
Dioxipe Dioxipe from
the Elpenor site
Galilee Unicode Gk Galilee Unicode Gk by
Rodney J. Decker
Gandhari Unicode Gandhari Unicode from
the Early Buddhist Manuscripts Project
New Athena Unicode New Athena Unicode from
the GreekKeys site
The rest are all missing some numerals:
Aisa Unicode Aisa Unicode, packaged with
the MultiKey utility
Alkaios Alkaios by
Lucius Hartmann
Asteria Asteria from
the Elpenor site
Caslon Caslon by
George Williams
Chrysanthi Unicode Chrysanthi Unicode by
D. Paul Alecsandri
FreeSerif FreeSerif from
the Free Software Foundation, Inc.
Galatia SIL Galatia SIL from
Galatia SIL Greek Unicode Fonts
GentiumAlt GentiumAlt by
Victor Gaultney
Would be my choice for a “big” Unicode font, if it had numerals and a handwritten theta.
Georgia Greek Georgia Greek, available at
Christos A. Sartzetakis' site or the Elpenor site
GFS Artemisia GFS Artemisia from
the Greek Font Society
GFS Bodoni Rg GFS Bodoni Rg from
the Greek Font Society
GFS Didot Rg GFS Didot Rg from
the Greek Font Society
GFS Elpis GFS Elpis from
the Greek Font Society
GFS Neohellenic Rg GFS Neohellenic Rg from
the Greek Font Society
GFS Olga GFS Olga from
the Greek Font Society
GFS Porson GFS Porson from
the Greek Font Society
Legendum Legendum by
Rogier van Dalen
The larger font, Legendum_legacy.otf, uses precomposed characters.
Minion Pro Minion Pro
Packaged with Acrobat 7; find it in the Acrobat folder, such as C:\Program Files\Adobe\Acrobat 7.0\Resource\Font
Monospace Monospace by
George Williams
I uninstalled this font because it conflicts with the CSS generic family specifier of the same name.
Palatino Linotype Palatino Linotype
Packaged with Windows XP/2000; also commercially available.
Porson Porson by
Richard G. Spaulding
This font did not display in IE5.5
Thryomanes Thryomanes by
Herman Miller
Works in Word and Firefox, but not IE6 on my computer.
TITUS Cyberbit Basic TITUS Cyberbit Basic from
the TITUS site
Vusillus Old Face Italic Vusillus Old Face Italic by
Ralph Hancock
Code2000 is widely distributed, and is actually shareware ($5).
code2000 Code2000 by
James Kass
Juan-José Marcos was kind enough to send me his font, Alphabetum, to try out.  The demo is free, but there is a charge for the full working copy.
Alphabetum Alphabetum by
Juan-José Marcos
Besides Greek, it contains many other ancient fonts such as Runic, Sanskrit, Iberian, Old Nordic, Ugaritic, Phoenician, and cuneiform, to name a few.

*For some reason, most font designers today use a tilde instead of the round, Porsonic circumflex accent.  This never looks right to me, and it provides less space for a breathing mark.  I also like handwritten-like theta and phi, simple zeta and xi, a small loop in gamma, a not-too-fancy psi, middle and final sigmas that look as much alike as possible (like modified lunate sigma, written like a “c”), and fairly simple design in general.  For the capital letters, I prefer the rounded upsilon and a fairly long bar in theta.  Thus, the Aristarcoj font.

The current release is Aristarcoj version 2.  I have updated it with all the characters added to the Unicode standard on the Greek and Coptic, and Greek extended, code charts since the first version was released in 2002.  I have also added some additional characters such as double brackets.  The only glyph which was changed in the sample above is capital sampi Ϡ.  When I first made Aristarcoj, there were very few other fonts available which contained all the archaic numerals, and I followed David Perry's example by using an “M”-like glyph for this character.  Now, however, the Unicode standard suggests this shape for the new character san, so I used my former glyph Ϻ for this character, and bowed to the prevailing trend by creating a large Pi-like glyph for sampi.

I worked some more on the combining diacritical marks; someone who actually uses them will have to let me know if they are working properly.  α̣ ῃ ΐ ὄ ὑ̂  (They seem to have had some problems in the first release.)  I confess that I am still not clear on the concept of why one would want to make much use of them when the purpose of Unicode is to provide places for all the preformed characters.

Additionally, I reduced the slant of the characters a little, and scaled the font up slightly so that it fits better with common Latin fonts.  Being a “homemade” font, I do not expect that it will meet high professional standards.  The characters still have a slight slant, and it therefore does not hint well, and is still not hinted at all, like several of the others above.  It prints well, though.  View it in .pdf format (52kb; get Acrobat Reader).

For Greek fonts in general, which tend to have lots of curves, tell your computer to “smooth edges of screen fonts” if they appear jagged on-screen.  Clear Type will produce very smooth results.