Here is a list of combinations of Lisp implementation and operating system which are known to run Maxima.

Key:

MS Windows

Windows installer: http://sourceforge.net/project/showfiles.php?group_id=4933.

GCL
Clisp

GNU/Linux — Fedora

Binaries
GCL
Clisp
SBCL
CMUCL
Various combinations work.
Scieneer-CL

GNU/Linux — Slackware

Binaries
GCL
Clisp
SBCL
CMUCL

Many other version combinations work as well but have not been well (or recently) tested.

GNU/Linux — Gentoo

Clisp

Various combinations with other Lisp implementations work, too. Which Lisp implementation to choose can be controlled by the package’s USE flags clisp, cmucl, gcl and sbcl. To install, just type as root: emerge sci-mathematics/maxima.

GNU/Linux — Debian

(Maxima page http://packages.debian.org/unstable/math/maxima lists a lot of platforms, although it doesn’t mention Lisp implementations.)

MacOS X

Building Maxima from source code:

Clisp
Clisp 2.41 + Maxima 5.12.0 — A-OK
SBCL
CMUCL
Fink
MacPorts

FreeBSD

These all build from the FreeBSD ports system:

CLISP
CMUCL
GCL
SBCL

These build from cross-platform pkgsrc system:

CLISP
SBCL
ECL

NetBSD