The American Mathematical Society has compiled this list of cross-platform TeX editors for user convenience; we do not offer support for these programs. All of this software presupposes that a complete TeX installation (such as TeXLive) exists on your computer.
Unless otherwise noted, the tools listed here are free.
Platforms: Windows, Linux, Mac OS X, Gnome 3
Texmaker runs smoothly and has a user-friendly interface.
Platforms: Windows, Linux, Mac OS X
TeXworks is still in beta -- a work-in-progress -- but is generally solid and usable. It is an excellent attempt to bring the elegant interface of TeXShop for Mac OS X to a cross-platform environment.
Platforms: Windows, Mac OS X, Linux
LyX is referred to as a "what you see is what you mean" LaTeX editor; some aspects of LaTeX are hidden behind the interface. This program works well for those who are not interested in delving into TeX's inner workings.