About Ambigrams
Ambigrams are typographical optical illusions that display one message
in one orientation and the same message (called an "ambigram") or a different
message (called a "symbiotogram") in another orientation.
The most common ambigram form is a 180 degree rotational design that
displays one message when the design is upright and another message when the design
is upside-down.
The first published reference to the word "ambigram" is attributed to
Douglas Hofstadter, who states that the word was coined during
conversations he had with his friends in 1983.
Ambigram Types
Although rotational ambigrams are the most common form, an
"ambigram" is any word form designed to be viewed from a plurality of
view points. Some of the other ambigram forms are (in order of
commonality):
Rotational
This most common ambigram type allows designs to be viewed from
multiple orientations that differ by viewpoint angle. Typically, this is a 180 degree rotation,
but ambigrams have been created with 90 degree rotation, and other fixed
angle rotations are possible (although rare). When the word in the
alternate direction is the same as the original word, it is called simply an
"ambigram", but when the two words are different, the design is
commonly called a "symbiotogram".
The rotational ambigram design received a huge surge in popularity with
the release of Dan Brown's Vatican thriller book "Angels and Demons",
which featured six rotational ambigrams of Illuminati, Earth, Air,
Fire, Water and a multi-word ambigram of those four elements called the
Illuminati Diamond, all drawn by ambigram artist John Langdon.
[The Illuminati Diamond, ©1999 John Langdon]
Mirror
A design that displays one message when read directly, and a
second message when read in a mirror or through a piece of glass, such
as a window (see mirror ambigram of the words "front" and "back").
Figure-ground
Figure-ground ambigrams do not require a shift in orientation, only
a shift in perception. In a figure-ground ambigram, the two designs
are presented in the same physical space where the spaces between the
letters in one word become the form of a second word, and vice versa.
Circle or Chain
A circle or chain ambigram is a series of words (the same or
different), which are linked together in such a way that they form a
repeating pattern, which is often arranged in the form of a circle or
interlocking grid.
Symbiotogram
The word "symbiotogram" almost always refers to a 180 degree
rotational ambigram, where the words in the upright and inverted
orientations are different words (see symbiotogram of the words "TRUE" and "FALSE").
[True/False ambigram, © 2000 John Langdon]
Technology
Although the ambigram space has typically been the arena of
talented artists, some progress has been made to develop software that
can generate some impressive works.
The first letter inversion script on the Internet was the
"ambimatic" in 1995, which could take any two words of equal lengths and create
a rough inversion of the letters in the words.
The first real ambigram generator in the Internet was released in June, 2008, as a joint venture between a software developer and an ambigram artist working under the name "Glyphusion". Capable of combining words of non-equal lengths and generating ambigrams containing multi-character glyphs, the system was able to successfully replicate the steps that an ambigram artist would take in creating a design, including evaluating options for create the design, drawing an outline of the letters, fitting them together, filling them with color and rendering them to a surface (typically a JPG graphic). In many cases, the Glyphusion Generator was able to produce ambigram designs equal to or superior to human designs.
You can create your own ambigram using the FlipScript
ambigram generator
Famous Ambigrams
Several ambigrams have become band, product or company logos, or have otherwise been put into use as a brand. While an exhaustive list of all in-use ambigrams would be close to impossible, several popular designs are listed below:

One form of the Aerosmith Band Logo
[Aerosmith ambigram, ©2003 Dan Brown and John Langdon]

New Man clothing

Vista Service Corps

Chump Matches
The Olympic Games Committee even had an ambigram design as a logo finalist for the 2012 London games:
Commercial Ambigrams on the Web
Here are some other examples of ambigrams "in use" on the Internet
Epoch
Jaier
topdot
Mensa