Planet Perplex has several of these:http://www.planetperplex.com/en/sliding_puzzles.html
Livewire has a free version at:http://www.puzzles.ca/magical_envelope_puzzle.html
The vanishing Ninja:http://www.dojopress.com/tvn.html
You can buy several version at Archimedes' Lab:http://www.cafepress.com/mariejo2/345778
They call them "geometric erodings" or "stereophanic puzzles"http://www.archimedes-lab.org/page5b.html#http://www.archimedes-lab.org/page7b.html
You can print one:http://www.archimedes-lab.org/workshopvanishbird.htmlhttp://www.archimedes-lab.org/Gallery/new_optical_illusions/pages/101-Magic_eggs_VAN.html
There is an explanation of the Vanishing Leprechaun at this site:http://britton.disted.camosun.bc.ca/jblep1.htm
It was designed by Ms. Pat (Patterson) Lyons circa 1968 and is related to the DeLand Paradox.
Other geometrical paradoxes are illustrated here:http://library.thinkquest.org/28049/geometrical_vanishes.htm
Here is a video of one classic geometric fallacy:http://www.youtube.com/watch?v=sDerqFGmwNI
"Who Turned to Doggie Doo?" by Robin Debreuil is nice entertaining example of a vanish.
You can see it on John Rausch's site here:http://www.puzzleworld.org/PuzzleWorld/puz/who_turned_to_doggie_doo.htm
and at Debreuil's site:http://debreuil.com/ddw/puzjava/picmove.htm
where you can download a free printable version.
The Magic Egg is another classic - see it here (requires Shockwave plugin):http://www.psychologie.tu-dresden.de/i1/kaw/diverses%20Material/www.illusionworks.com/html/vanishing_egg.html
The actual antique postcard can sometimes be found on eBay.
That site also has an explanation of how these puzzles work.
It also mentions a criminal use of the vanish:
" The principle is very old and probably originated as a early method for counterfeiting money. William Hooper in his book Rational Recreations, published in 1794, described the paradox as "Geometric Money," It is possible to cut 9 bills into eighteen parts (following the pattern of the lines) and then to rearrange them to make ten bills. To foil this method, the two numbers on all U.S. currency is placed on opposite ends, one high and one low. In this way, counterfeit bills using this method are easy to detect since their numbers will not match correctly. In fact, in 1968, a man in London was sentenced to eight years in prison for using this scheme on British five-pound notes."
I think it is interesting how Pat Lyons came out with the Leprechauns in 1968! Coincidence?
Two informative articles are a section in Martin Gardner's Mathematics, Magic and Mystery (1958) and an article by Mel Stover in the November 1980 issue of Games magazine.
Also discussed in Gardner's "Wheels, Life, and Other Mathematical Amusements" in chapter 12.
Martin Gardner calls it "the principle of concealed distribution."
Try Mel Stover's Pencils here:http://www.puzzles.com/puzzleplayground/StoversPencils/StoversPencils.htm
Check out a version by Mark Setteducati here:http://www.marksetteducati.com/apeardisapear.htm
See a great trick by Masao Atsukawa called Warp 9:http://www.youtube.com/watch?v=nvUpFC49oFM
Winston Freer's Tile Puzzle:http://www.youtube.com/watch?v=_LY7mf49l5k
a similar effect:http://www.youtube.com/watch?v=uMIm2Md4uIA
You can find that trick sold on eBay
A fun version at the dharmainitiative:http://www.dharmainitiative.it/index.php?id=test&n=8
That site also provides info on the history of the vanish:
"The first example of vanishing area puzzles was reported in the book Libro d'Architettura Primo by Sebastiano Serlio (1475-1554)"
"The first description and mathematical explanation of the vanish paradox was found in a math puzzle book with a very long title: Rational Recreations: In which the Principles of Numbers and Natural Philosophy are Clearly and Copiously Elucidated, by a Series of Easy, Entertaining, Interesting Experiments. Among which are All Those Commonly Performed with the Cards, L. Davis; J. Robson; B. Law; and G. Robinson, 1774 by William Hooper. Probably Hooper cribbed the puzzle from the book Nouvelles récréations physiques et mathématiques by the French author Edmé Gilles Guyot (1770)"
And gives links to download the book from google:http://books.google.it/books?id=mGxbAAAAQAAJ&dq=william%20hooper%20Rational%20Recreations&pg=PA286#v=onepage&q&f=false
You can buy copies of Sam Loyd's vanish puzzles, and try them online, here:http://www.samuelloyd.com/http://www.samloyd.com/vanishing-puzzles/index.html
The Jerry Slocum collection at the Lilly Library contains a few:http://webapp1.dlib.indiana.edu/slocum/results/result.do?display=thumbcap&action=browse&page=1&pagesize=20&query=collection%3Alilly%2Fslocum+classification:8*
I have a copy of the vintage French boxed puzzle "L'Echiquier Fantastique"