Pushdown automaton
A Wikipedia article with a definition and simple example.
http://en.wikipedia.org/wiki/Pushdown_automaton

Linear-bounded Automaton
Example of construction of an LBA to accept a particular context free language.
http://www.everything2.com/index.pl?node_id=1394039

CAGE
A generic and extensible cellular automaton simulation engine written in Python.
http://www.alcyone.com/software/cage/

Linear Bounded Automaton
Wikipedia article defines LBA and shows their place in the Chomsky hierarchy.
http://en.wikipedia.org/wiki/Linear_bounded_automaton

WolframTones
WolframTones: A New Kind of Music -- Unique cellphone ringtones and music created by simple programs from renowned scientist Stephen Wolfram's computational universe
http://tones.wolfram.com/

Automaton Wars
Peter Hartley's freeware strategy game (similar to Explosion or Atoms) for Acorn RiscOS computers
http://utter.chaos.org.uk/~pdh/software/autowars.htm

Isle Ex Applet Cellsprings-Web
A general 2D cellular automaton explorer implemented as a Java 1.1 applet. By John Elliott.
http://jmge.net/java/csprings/

Universal Cellular Automaton
A Java Applet for simulating all kind of cellular automata, including Conway's Game Of Life or snowflake generation rules. By Frank Buß.
http://www.frank-buss.de/automaton/index.html

Cellular Automaton Music
Music samples generated using some popular cellular automata rules; by John Elliott.
http://jmge.net/camusic.htm

jrexx
A regular expression API for textual pattern matching based on the finite state automaton theory written in Java. It also offers set operations (union, intersection, difference, complement) for combination of automatons. [Open source, LGPL]
http://www.karneim.com/jrexx/project01/project01.htm