Choice of scalable outline fonts
If you are interested in text alone, you can use any of over 20,000
fonts(!) in Adobe Type 1 format (called 'PostScript fonts' in the
TeX world and 'ATM fonts' in the DTP world), or any of several
hundred fonts in TrueType format.  That is, provided of course, that
your previewer and printer driver support scalable outline fonts.
TeX itself only cares about metrics, not the actual
character programs.  You just need to create a TeX metric file
TFM using some tool such as afm2tfm (possibly in
combination with vptovf), afmtotfm
(from Y&Y, see
commercial implementations)
or fontinst.  For the previewer or printer driver you need the
actual outline font files themselves (pfa for Display PostScript, pfb
for ATM on IBM PC, Mac outline font files on Macintosh).
If you also need mathematics, then you are severely limited by the
demands that TeX makes of maths fonts (for details, see the paper by B.K.P. 
Horn in TUGboat 14(3)).
For maths, then, there are relatively few choices (though the list is
at last growing).  There are several font families available that are
based on Knuth's original designs, and some that complement other
commercial text font designs; one set (MicroPress's 'informal math')
stands alone.
- Computer Modern
- (75 fonts - optical scaling) Donald E. Knuth
 The CM fonts were originally designed in Metafont, but are also
  now available in scalable outline form.  There are commercial as
  well as public domain versions, and there are both Adobe Type 1 and
  TrueType versions.  A set of outline versions of the fonts was
  developed as a commercial venture by Y&Y and Blue Sky Research;
  they have since assigned the copyright to the AMS, and the
  fonts are now freely available from CTAN.  Their quality is
  such that they have become the de facto standard for Type 1
  versions of the fonts.
- AMS fonts
- (52 fonts, optical scaling) The AMS
 This set of fonts offers adjuncts to the CM set, including
  two sets of symbol fonts (msamandmsbm) and Euler text fonts.
  These are not a self-standing family, but merit discussion here (not
  least because several other families mimic the symbol fonts).
  Freely-available Type 1 versions of the fonts are available on
  CTAN.  The eulervm package permits use
  of the Euler maths alphabet in conjunction with text fonts that do
  not provide maths alphabets of their own (for instance, Adobe
  Palatino or Minion).
- Computer Modern Bright
- (62 fonts - optical scaling) Walter
  Schmidt
 CM Bright is a family of sans serif fonts, based on Knuth's
  CM fonts.  It comprises the fonts necessary for mathematical
  typesetting, including AMS symbols, as well as text and text
  symbol fonts of various shapes.  The collection comes with its own
  set of files for use with LaTeX.  The CM Bright fonts are
  supplied in Type 1 format by MicroPress, Inc.; free versions are
  available on CTAN - the hfbright set for use with
  text using OT1 encoding and the cm-super set for
  use with T1.  
  For further details of Micropress' offering (including samples) see
 http://www.micropress-inc.com/fonts/brmath/brmain.htm
 
- Concrete Math
- (25 fonts - optical scaling) Ulrik Vieth
 The Concrete Math font set was derived from the Concrete Roman
  typefaces designed by Knuth.  The set provides a collection of math
  italics, math symbol, and math extension fonts, and fonts of
  AMS symbols that fit with the Concrete set, so that Concrete
  may be used as a complete replacement for Computer Modern.  Since
  Concrete is considerably darker than CM, the family may
  particularly attractive for use in low-resolution printing or in
  applications such as posters or transparencies.  Concrete Math
  fonts, as well as Concrete Roman fonts, are supplied in Type 1
  format by MicroPress, Inc.  
  For further information (including samples) see
 http://www.micropress-inc.com/fonts/ccmath/ccmain.htm
 
- BA Math
- (13 fonts) MicroPress Inc.
 BA Math is a family of serif fonts, inspired by the elegant
  and graphically perfect font design of John Baskerville.  BA
  Math comprises the fonts necessary for mathematical typesetting
  (maths italic, math symbols and extensions) in normal and bold
  weights.  The family also includes all OT1 and T1
  encoded text fonts of various shapes, as well as fonts with most
  useful glyphs of the TS1 encoding.  Macros for using the
  fonts with Plain TeX, LaTeX 2.09 and current LaTeX are
  provided.  
  For further details (including samples) see
 http://www.micropress-inc.com/fonts/bamath/bamain.htm
 
- HV Math
- (14 fonts) MicroPress Inc.
 HV Math is a family of sans serif fonts, inspired by the
  Helvetica (TM) typeface.  HV Math comprises the fonts
  necessary for mathematical typesetting (maths italic, maths symbols
  and extensions) in normal and bold weights.  The family also
  includes all OT1 and T1 encoded text fonts of various
  shapes, as well as fonts with most useful glyphs of the TS1
  encoding.  Macros for using the fonts with Plain TeX, LaTeX 2.09
  and current LaTeX are provided.  Bitmapped copies of the fonts
  are available free, on CTAN.  
  For further details (and samples) see
 http://www.micropress-inc.com/fonts/hvmath/hvmain.htm
 
- Informal Math
- (7 outline fonts) MicroPress Inc.
 Informal Math is a family of fanciful fonts loosely based on the
  Adobe's Tekton (TM) family, fonts which imitate handwritten
  text.  Informal Math comprises the fonts necessary for
  mathematical typesetting (maths italic, maths symbols and extensions)
  in normal weight, as well as OT1 encoded text fonts in
  upright and oblique shapes.  Macros for using the fonts with
  Plain TeX, LaTeX 2.09 and current LaTeX are provided.  
  For further details (including samples) see
 http://www.micropress-inc.com/fonts/ifmath/ifmain.htm
 
- Lucida Bright with Lucida New Math
- (25 fonts) Chuck Bigelow and
  Kris Holmes
 Lucida is a family of related fonts including seriffed, sans serif,
  sans serif fixed width, calligraphic, blackletter, fax, Kris Holmes'
  connected handwriting font, etc; they're not as 'spindly' as
  Computer Modern, with a large x-height, and include a larger set of
  maths symbols, operators, relations and delimiters than CM
  (over 800 instead of 384: among others, it also includes the
  AMSmsamandmsbmsymbol sets).  'Lucida Bright Expert'
  (14 fonts) adds seriffed fixed width, another handwriting font,
  smallcaps, bold maths, upright 'maths italic', etc., to the
  set.  The distribution includes support for use with Plain TeX
  \acro{PSNFSS} (\Qref{}{Q-usepsfont}) 
  PSNFSS
  thanks to Sebastian Rahtz and David Carlisle.  
  For a sample, see http://www.YandY.com/download/chironlb.pdf
  
 
- MathTime 1.1
- (3 fonts) Publish or Perish (Michael Spivak)
 The set contains maths italic, symbol, and extension fonts, designed
  to work well with the Times-Roman family, which is resident on many
  printers, and which is supplied with some PC versions.  In
  addition you may want to complement this basic set with Adobe's
  Times Smallcap, and perhaps the set of Adobe 'Math Pi' fonts, which
  include blackboard bold, blackletter, and script faces.  
  For a sample, see http://www.YandY.com/download/chironmt.pdf
  
 
- MathTime Plus
- (12 fonts) Publish or Perish (Michael Spivak)
 Adds bold and heavy versions of the basic math fonts, as well as
  upright math "italic".  There are also Greek letters for use in
  typesetting terms commonly used in physics, as well as regular and
  bold script faces.  Both MathTime distributions include support for
  use with Plain TeX and LaTeX 2.09 (including code to link in
  Adobe Math Pi 2 and Math Pi 6).  Support under LaTeX2e is provided
  in
  PSNFSS
  thanks to Frank Mittelbach and David Carlisle.  
  For a sample, see http://www.YandY.com/download/mathplus.pdf
  
 
- TM Math
- (14 fonts) MicroPress Inc.
 TM Math is a family of serif fonts, inspired by the Times
  (TM) typeface.  TM Math comprises the fonts necessary for
  mathematical typesetting (maths italic, maths symbols and extensions)
  in normal and bold weights. The family also includes all OT1
  and T1 encoded text fonts of various shapes, as well as fonts
  with most useful glyphs of the TS1 encoding.  Macros for
  using the fonts with Plain TeX, LaTeX 2.09 and current LaTeX
  are provided.  Bitmapped copies of the fonts are available free, on
  CTAN.  
  For further details (and samples) see
 http://www.micropress-inc.com/fonts/tmmath/tmmain.htm
 
- Belleek
- (3 fonts) Richard Kinch
 Belleek is the upshot of Kinch's thoughts on how Metafont might be used
  in the future: they were published simultaneously as Metafont source,
  as Type 1 fonts, and as TrueType fonts.  The fonts act as "drop-in"
  replacements for the basic MathTime set (as an example of "what might
  be done").  The paper outlining Kinch's thoughts, proceeding from considerations
  of the 'intellectual' superiority of Metafont to evaluations of why its
  adoption is so limited and what might be done about the problem, is
  to be found at http://truetex.com/belleek.pdf (the paper is a
  good read, but exhibits the problems discussed in
  
  "getting good PDF" -
  don't try to read it on-screen in Acrobat reader).
 
- PA Math
-  PA Math is a family of serif fonts
  loosely based on the Palatino (TM) typeface.  PA Math
  comprises the fonts necessary for mathematical typesetting (maths
  italics, maths, calligraphic and oldstyle symbols, and extensions)
  in normal and bold weights. The family also includes all OT1,
  T1 encoded text fonts of various shapes, as well as fonts
  with the most useful glyphs of the TS1 encoding.  Macros for
  using the fonts with Plain TeX, LaTeX 2.09 and current LaTeX
  are provided.
  
  For further details (and samples) see
 http://www.micropress-inc.com/fonts/pamath/pamain.htm
 
- mathpazoversion 1.003
- (5 fonts) by Diego Puga
 The Pazo Math fonts are a family of type 1 fonts suitable for
  typesetting maths in combination with the Palatino family of text
  fonts.  Four of the five fonts of the distribution are maths
  alphabets, in upright and italic shapes, medium and bold weights;
  the fifth font contains a small selection of "blackboard bold"
  characters (chosen for their mathematical significance).  Support
  under LaTeX2e is available in 
  PSNFSS; the fonts are
  licensed under the GPL, with legalese permitting the use of
  the fonts in published documents.
- pxfontsset version 1.0
- (26 fonts) by Young Ryu
 Thepxfontsset consists of
  -  virtual text fonts using Adobe Palatino (or the URW
    replacement used by ghostscript) with modified plus,
    equal and slash symbols;
  
-  maths alphabets using times;
  
-  maths fonts of all symbols in the computer modern maths fonts
    (cmsy,cmmi,cmexand the Greek letters ofcmr)
-  maths fonts of all symbols corresponding to the AMS
    fonts (msamandmsbm);
-  additional maths fonts of various symbols.
  
 The text fonts are available in OT1, T1 and LY1
  encodings, and TS encoded symbols are also available.  The
  sans serif and monospaced fonts supplied with thetxfontsset (see below) may be used withpxfonts; thetxfontsset should be installed wheneverpxfontsare.  LaTeX, dvips and PDFTeX support files are
  included.  The
  documentation
  is readily available.  The fonts are licensed under the GPL; use in published
  documents is permitted.
 
- txfontsset version 3.1
- (42 fonts) by Young Ryu
 Thetxfontsset consists of
  -  virtual text fonts using Adobe Times (or the URW
    replacement used by ghostscript) with modified plus,
    equal and slash symbols;
  
-  matching sets of sans serif and monospace ('typewriter')
    fonts (the sans serif set is based on Adobe Helvetica);
  
-  maths alphabets using times;
  
-  maths fonts of all symbols in the computer modern maths fonts
    (cmsy,cmmi,cmexand the Greek letters ofcmr)
-  maths fonts of all symbols corresponding to the AMS
    fonts (msamandmsbm);
-  additional maths fonts of various symbols.
  
 The text fonts are available in OT1, T1 and LY1
  encodings, and TS encoded symbols are also available.
  LaTeX, dvips and PDFTeX support files are included.
  The
  documentation
  is readily available.  The fonts are licensed under the GPL; use in published
  documents is permitted.
 
- Adobe Lucida, LucidaSans and LucidaMath
- (12 fonts)
 Lucida and LucidaMath are generally considered to be a bit heavy.
  The three maths fonts contain only the glyphs in the CM maths
  italic, symbol, and extension fonts.  Support for using LucidaMath
  with TeX is not very good; you will need to do some work
  reencoding fonts etc.  (In some sense this set is the
  ancestor of the LucidaBright plus LucidaNewMath font set.)
- Proprietary fonts
- Various sources.
 Since having a high quality font set in scalable outline form that
  works with TeX can give a publisher a real competitive advantage,
  there are some publishers that have paid (a lot) to have such font
  sets made for them.  Unfortunately, these sets are not available on
  the open market, despite the likelihood that they're more complete
  than those that are.
- Mathptmx
- Alan Jeffrey, Walter Schmidt and others.
 This set contains maths italic, symbol, extension, and roman virtual
  fonts, built from Adobe Times, Symbol, Zapf Chancery, and the
  Computer Modern fonts.  The resulting mixture is not  entirely
  acceptable, but can pass in many circumstances.  The real advantage
  is that the mathptm fonts are (effectively) free, and the resulting
  PostScript files can be freely exchanged.  Support under LaTeX2e
  is available in 
  PSNFSS.
The very limited selection of commercial maths font sets is a direct result of
the fact that a maths font has to be explicitly designed for use with
TeX and as a result it is likely to lose some of its appeal in
other markets. Furthermore, the TeX market for commercial fonts is
minute (in comparison, for example, to Microsoft TrueType font pack 1,
which sold something like 10 million copies in a few weeks after 
release of Windows 3.1!).Text fonts in Type 1 format are available from many vendors including
Adobe, Monotype and Bitstream.  Avoid cheap rip-offs: not only are you
rewarding unethical behaviour, destroying the cottage industry of
innovative type design, but you are also very likely to get junk.
The fonts may not render well (or at all under ATM), may not have the
'standard' complement of 228 glyphs, or may not include metric files
(needed to make TFM files).
TrueType remains the "native" format for Windows.  Some TeX
implementations such as 
TrueTeX use TrueType versions of
Computer Modern and Times Maths fonts to render TeX documents in
Windows without the need for additional system software like
ATM.
When choosing fonts, your own system environment may not be the only one of
interest.  If you will be sending your finished documents to others for
further use, you should consider whether a given font format will introduce
compatibility problems.  Publishers may require TrueType exclusively because
their systems are Windows-based, or Type 1 exclusively, because their systems
are based on the early popularity of that format in the publishing industry.
Many service bureaus don't care as long as you present them with a finished
print file (PostScript or PDF) for their output device.
- CM family collection
- 
  Browse fonts/cm/ps-type1/bluesky/
- AMS font collection
- 
  Browse fonts/amsfonts/ps-type1/
- Belleek fonts
- 
  fonts/belleek/belleek.zip
- CM-super collection
- fonts/ps-type1/cm-super (zip, browse)
- eulervm.sty and supporting metrics
- 
  fonts/eulervm (zip, browse)
- hfbright collection
- fonts/ps-type1/hfbright (zip, browse)
- hvmath (free bitmapped version)
- 
  fonts/micropress/hvmath (zip, browse)
- pxfonts
- fonts/pxfonts (zip, browse)
- tmmath (free bitmapped version)
- 
  fonts/micropress/tmmath (zip, browse)
- txfonts
- fonts/txfonts (zip, browse)
This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=psfchoice