I've done this game on a couple of the forums I run, and it's proven to be a hit. Whilst it's totally not politically correct, it's still really addictive. It's called
Find the Hitler!
Here's how to play it:
Go to
Wikipedia, and click
Random Article. Then following links in that page and subsequent pages, get to Adolf Hitler by the shortest route, or for added bonus points, by the most convoluted route - that being a route of 15 or more clicks.
Different people can use the same page twice, but if you've already used a page in one route, you cannot use that page in subsequent routes!
Well. Here's mine:
Hill repair --> Pacific Northwest --> Greece --> Greeks in Germany --> Germany --> Adolf Hitler
Sweden-->Germany-->Adolf Hitler
Here's a 30-click route to Hitler, once again starting at the random article "Noctubourgognea coppingeri". I tried as much as I could to use the most tangential (ie. least topical) link on each page to maximize convolution. I'm sure I can go on much longer, but I got sick of it around "Taro".
Noctubourgognea coppingeri
Moth
Moon
Angular momentum
Electromagnetic field
CD players
SCSI
Cyclic redundancy check
MITRE
Not-for-profit
Art
Ming Dynasty
Peanut
Cardiovascular disease
Physical exercise
Cognition
Education
Writing
Manuscript
Mummy
Starfish
Deepwater Horizon spill
Fifth Amendment to the United States Constitution
Magna Carta
Bishops
Cyprus
Taro
Brazil
Germany
Adolf Hitler
------------------------------------
I think it would be more interesting to try to reach Adolph Hitler without going through obvious pages on Germany or Nazi or related topics. Maybe I'll try that next.
John Archibald Maharg
Legislative Assembly of Saskatchewan
Cumulative voting
Consistency criterion
Simpson's paradox
United States Department of Education
Institute of Education Sciences
National Library of Education (United States)
United States Secretary of Education
Rod Paige
September 11 attacks
List of intelligence agencies of Germany
Bundesnachrichtendienst
Bundeswehr
Adolf Hitler
Okay, here's a convoluted attempt to go from "Lemmings" to Hitler:
Lemmings (video game)
The Good, the Bad and the Ugly
PCF theory
Power set
Multigraph
Ordered pair
Coordinate system
Galilean transformation
Ball
Kitten
Average
Domesday Book
Honey
Radioactive decay
Avalanche
Pyroclastic flow
Sumatra
Marco Polo
Coal
Lewis and Clark Expedition
Beaver
Israel
Bible
Kabbalah
Tiferet
Abracadabra
J. K. Rowling
Monty Python
Tim Curry
Four Dogs Playing Poker
SAV
Erwan Vallerie
Nono
List of Planetes characters
Cattle mutilation
Space Invaders
List of Robot Chicken episodes
Adolf Hitler
=======
I started with "Lemmings" and did the same thing as last time, but right around when I got to "Beaver", I thought I should start from the end and try to make the links into Hitler as unrelated to Germany or Nazi etc. as possible. So I did that, making use of the "What links here" feature of Wikipedia. That eventually leads up to "Bible", and surprisingly it was only 2 clicks to go from "Beaver" to "Bible", so boom!
I do think making Hitler the endpoint makes the game a little too easy. A comparatively more esoteric topic like "Lemmings" might make for a more interesting endpoint for this sort of game.
And in case anyone wonders, here's the shortest clicks from Lemmings to Hitler I can find:
Lemmings (video game)
Jacques Offenbach
Germany
Adolf Hitler
Yep, you have the Can-can music to thank for this extra-short connection to Hitler.
Fritz Aigner -> Linz -> Hitler
well that was disappointingly easy

EDIT: Very next attempt:
Boden Fortress -> Hitler
Oh come on next time I'm going to get Hitler as my random click
I hereby state a theory:
From any random Wikipedia article, you can reach the Adolf Hitler article with 3 clicks or less.
Setshele I -> Botswana -> South Africa -> Kingdom of Great Britain -> United Kingdom -> Continental Europe -> Europe -> Adolf Hitler
Baleària -> Spain -> List of languages by number of native speakers -> German Language -> Germany -> Nazi Germany -> Adolf Hitler
. . . Maybe a bit too easy. We should probably get a slightly different endpoint.
Any suggestions?
...allow me to state the obvious, and suggest Lemmings.
Rango Narayan Orpe → Shivaji → Hindu → Swastika → Adolf Hitler
Sustenhorn → Switzerland → Adolf Hitler
Panchlaish Thana → Bangladesh → Genocide → The Holocaust → Adolf Hitler (surprisingly, "Genocide" only mentions Hitler, and doesn't link to him. Of course, I could always go and edit it so that it does.....)
Ounceland → Markland (Scots) → Deutsche Mark → Germany → Adolf Hitler
Golden Monarch → Indonesia → Dutch East Indies → World War II → Adolf Hitler
Nikon Instruments → Tokyo → World War II → Adolf Hitler
...allow me to state the obvious, and suggest Lemmings.
ccexplore posted a shorter one, going through Offenbach, but I went
Lemmings → Rockstar North → United Kingdom → Germany → Hitler
You misunderstood namida. He's talking about the variation where you end with Lemmings while starting with a random article, ie.
?? → ... → Lemmings.
You misunderstood namida. He's talking about the variation where you end with Lemmings while starting with a random article, ie.
?? → ... → Lemmings.
Oh.

I imagine that would be much more difficult. Most things have a least one country link that you can follow to Germany and thus Hitler. There aren't a lot of things that would need to link to Lemmings.
Is using Special:Whatlinkshere a cheat?
I guess using special:whatlinkshere is not the way the original game was intended to be played, but I already used it once in this thread for assistance with creating entries into "Hitler" that doesn't go through the obvious candidates. It's just a forum game, go do whatever you feel makes it fun for you and everyone else.

I do believe though that it's a bit of a cheat to use links involving pages that aren't really articles, for example linking to/from things under Category: or Template: or User: or even Special: etc. Both endpoints in a link should be article pages only.
I usually edit wiki rather than play this game.

Anyway, here's my first attempt. (And not a bad one I don't think!)
Mount Royal, New Jersey
United States
Nazi Germany
Adolf Hitler
...allow me to state the obvious, and suggest Lemmings.
ccexplore posted a shorter one, going through Offenbach, but I went
Lemmings → Rockstar North → United Kingdom → Germany → Hitler
Ahem...
Lemmings → Richard Wagner → Adolf Hitler
Good catch! Once again, music has proven to be quite the shortcut into Hitler.
I'll try Lemmings 2.
Lemmings 2 → Musical instrument → Curt Sachs → Germany → Adolf Hitler
Music again...
If it comes to it,
Lemmings 2: The Tribes → Lemmings (video game) → Richard Wagner → Adolf Hitler
is shorter.

What you need to do is find a two-step link.
(Incidentally, even if you take out the trivial solution of going via Lemmings, I can find the three-step link
Lemmings 2: The Tribes → Cannon → World War II → Adolf Hitler
so yours still isn't the shortest

)
Wola Lipecka
Warmian-Masurian Voivodeship
East Prussia
Germany
World War II
Adolf Hitler
Random article:
Nils Olsson → Sweden → Winter War → Adolf Hitler
Flickering Flame: The Solo Years Volume 1 → Roger Waters → World War II → Adolf Hitler
Not random:
Burj Khalifa → United Arab Emirates → World War II → Adolf Hitler
If it comes to it,
Lemmings 2: The Tribes → Lemmings (video game) → Richard Wagner → Adolf Hitler
is shorter. 
What you need to do is find a two-step link.
(Incidentally, even if you take out the trivial solution of going via Lemmings, I can find the three-step link
Lemmings 2: The Tribes → Cannon → World War II → Adolf Hitler
so yours still isn't the shortest
)
It's been a while, but I thought I'd update with a couple of other ones:
Lemmings Paintball → Catapult → World War I → Adolf Hitler (3)
Lemmings Paintball → 1996 → Hitler Youth → Adolf Hitler (3)
Lemmings Paintball → 1996 → Artur Axmann → Adolf Hitler (the guy was the leader of the Hitler Youth and died in 1996) (3)
Christmas Lemmings → Christmas → South Tyrol → Adolf Hitler (3)
Oh No! More Lemmings → Sic → Appeal to ridicule → Reductio ad Hitlerum → Adolf Hitler (4)
Oh No! More Lemmings → Tutorial → Woodrow Wilson → World War I → Adolf Hitler (4)
Oh No! More Lemmings → Amiga → Japan → World War II → Adolf Hitler (4)
Oh No! More Lemmings → Amiga → Marilyn Monroe → (has the word "Hitler" in the text but not link

)
Oh No! More Lemmings → Amiga → Czech Republic → Adolf Hitler (3)
All New World of Lemmings → Buzzard → Common Buzzard → Japan → World War II → Adolf Hitler (5) (or via Amiga, same as ONML)
Had enough now. I just used a tool to find the opposite way:
Adolf Hitler → Russia → The Nutcracker → Lemmings (video game) (3)
One other interesting one I found:
Lemmings → Rockstar North → Daily Mail → Adolf Hitler
Comisión Nacional para el Conocimiento y Uso de la Biodiversidad
Felipe Calderón
Catholic Church
Soviet Union
Nazi Germany
Adolf Hitler
Unit (housing)
Statistics Canada
French language
Italy
Adolf Hitler
This is a fun game!
Random Article >> Lemmings
here are two and I didn't attempt to make the shortest list possible but more like the most random list possible. I didn't succeeded in either.
Surobi Nahgarhar
New York Times
video game
Atari
Atari ST
List of Atari ST games
Lemmings
here's one that's a random article to Lemmings but I also find Hitler on the way! (Getting to Scotland prooved to be more difficult than I imaged (why no links to Scotland?) and that didn't help anyway. Idk why I thought it would)
Liu Yudong
Senior Colonel
Kommodore
Nazi Germany
Adolf Hitler
Beer Hall Putsch
Germany
Europe
United Kingdom
History of Scotland
Red Clydeside
Riot Act
Crackdown
David Jones
Lemmings
I

at the random article I got.
Why the Bear Is Stumpy-Tailed
Norwegian Folktales
Denmark
Sydney's Opera House
Royal Botanic Gardens, Sydney
Arthur Phillip
Royal Marines
British Commandos
Immediate Reaction Cell
Logistics
Oxford English Dictionary
Guinness Book of World Records
Grand Theft Auto 4
Rockstar North
Lemmings
I love this game because I love randomness and you can learn stuff too

Official Languages of the United Nations
United Nations Economic and Social Council
Sven Markelius
1939 New York World's Fair
Louisiana Purchase Exposition
John Ireland (Archbishop)
Ancient Order of Hibernians
Saint Patrick's Day Parade
Shamrock
motif
egg-and-dart
Ovolo
Dorians
Acient Greece
Spain
Galicia (Spain)
Dundee
Lemmings
Patricio de la Escosura
playwright
Homophone
Dylan Thomas
Audio book
spoken-word album
Who's Afraid of Virginia Woolf?
Public domain
powered aircraft
weight distribution
free surface effect
RORO (roll-on/roll-off)
MS Color Magic
Kiel
1972 Summer Olympics
polymethyl methacrylate
Rohm and Hass
enterprise value
employee stock option
lattice model
trinomial tree
computational model
computational science
computing
video game consoles
Sega Genesis
list of Sega Genesis games
Lemmings
I was just clicking randomly until I got to "enterprise value" then decided I should actually find a way toward Lemmings. I didn't go backwards from Lemmings this time, in consequence it got kind of boring at the end.