So weird! I just closed/reopened my Terminal and tried "gem install gosu" again.

IT WORKED! It installed gosu with no errors. In the last few hours I changed the $PATH, putting /usr/local/bin before /usr/bin.

I also installed the gem "rubygame", Homebrew, and SDL:
https://github.com/rubygame/rubygame/wiki/Mac-Install-Guide

One of these things must have changed the environment somehow. Which was it?

Yes, I have all these frameworks in /System/Library/Frameworks on my Mac:

AudioToolbox.framework
OpenAL.framework
CoreFoundation.framework
ApplicationServices.framework

I still get this error message. Yes, I tried downloading your Gosu gem directly from http://rubygems.org/gems/gosu and installing that directly. This also did not work. Same error message.

Why is it not finding these frameworks? Where does it specify what path to look for them?

Here's my $PATH variable:

/usr/local/rvm/gems/ruby-1.9.3-p194/bin:/usr/local/rvm/gems/ruby-1.9.3-p194@global/bin:/usr/local/rvm/rubies/ruby-1.9.3-p194/bin:/usr/local/rvm/bin:/usr/local/bin:/usr/bin:/bin:/usr/sbin:/sbin:/opt/sm/bin:/opt/sm/pkg/active/bin:/opt/sm/pkg/active/sbin

Also, I'm not using a special compiler package. I just typed "gem install gosu"

Help! I cannot install the gosu Ruby gem on my Mac OS X (10.8.3).  I use Ruby 1.9.3p194. When I do "gem install gosu", I get all these compile errors.
It's true that I don't see the folders/files for OpenAL, CoreFoundation, ApplicationServices, Foundation, and AudioToolbox in my Ruby gem directory. Why not?

ERROR:  Error installing gosu:
  ERROR: Failed to build gem native extension.

    /usr/local/rvm/rubies/ruby-1.9.3-p194/bin/ruby extconf.rb
The Gosu gem requires some libraries to be installed system-wide.
See the following site for a list:
https://github.com/jlnr/gosu/wiki/Getting-Started-on-Linux

creating Makefile

make
compiling analysis.c
compiling bitrate.c
compiling bitwise.c
compiling block.c
compiling codebook.c
compiling envelope.c
compiling floor0.c
compiling floor1.c
compiling framing.c
compiling info.c
compiling lookup.c
compiling lpc.c
compiling lsp.c
compiling mapping0.c
compiling mdct.c
compiling psy.c
compiling registry.c
compiling res0.c
compiling sharedbook.c
compiling smallft.c
compiling synthesis.c
compiling vorbisfile.c
compiling window.c
compiling RubyGosu_wrap.cxx
In file included from ../Gosu/Gosu.hpp:13,
                 from RubyGosu_wrap.cxx:2227:
../Gosu/Fwd.hpp:10: warning: attribute ignored in declaration of ‘struct Gosu::Audio’
../Gosu/Fwd.hpp:10: warning: attribute for ‘struct Gosu::Audio’ must follow the ‘struct’ keyword
RubyGosu_wrap.cxx: In function ‘VALUE _wrap_Font_draw_rot(int, VALUE*, VALUE)’:
RubyGosu_wrap.cxx:5780: warning: ‘drawRot’ is deprecated (declared at ../Gosu/Font.hpp:79)
compiling AudioOpenAL.cpp
In file included from ../GosuImpl/Audio/AudioOpenAL.cpp:1,
                 from AudioOpenAL.cpp:1:
../GosuImpl/Audio/ALChannelManagement.hpp:3:23: error: OpenAL/al.h: No such file or directory
../GosuImpl/Audio/ALChannelManagement.hpp:4:24: error: OpenAL/alc.h: No such file or directory
In file included from ../GosuImpl/Audio/ALChannelManagement.hpp:5,
                 from ../GosuImpl/Audio/AudioOpenAL.cpp:1,
                 from AudioOpenAL.cpp:1:
../GosuImpl/MacUtility.hpp:6:42: error: CoreFoundation/CoreFoundation.h: No such file or directory
../GosuImpl/MacUtility.hpp:9:52: error: ApplicationServices/ApplicationServices.h: No such file or directory
In file included from AudioOpenAL.cpp:1:
../GosuImpl/Audio/AudioOpenAL.cpp:20:34: error: Foundation/Foundation.h: No such file or directory
In file included from ../GosuImpl/Audio/AudioOpenAL.cpp:21,
                 from AudioOpenAL.cpp:1:
../GosuImpl/Audio/AudioToolboxFile.hpp:5:39: error: AudioToolbox/AudioToolbox.h: No such file or directory
../GosuImpl/Audio/AudioToolboxFile.hpp:6:41: error: AudioToolbox/AudioConverter.h: No such file or directory
../GosuImpl/Audio/AudioToolboxFile.hpp:7:44: error: AudioToolbox/ExtendedAudioFile.h: No such file or directory

etc....