Don’t feel pathetic. This has generated much discussion among my friends. Kristie offered this explanation:
Then we went a few rounds of analysis, until my German-born-and-raised-in-Germany friend finally cleared it all up (it helps if you read all this in her adorable German accent):
Does that help? It’s starting to at least make sense to me, but it still isn’t funny! 
Ok, here’s a German joke I remember from circa 1987. I’ve updated it slightly but have had to keep certain parts in the original German for it to translate properly.
I might have told this one already, mmm… not sure.
Bush, Chirac, and Fischer, the leaders of The United States, France, and Germany are all together at a diplomatic meeting in an alpen village in Switzerland. A local Buerger tells Joschke Fischer of a very special outlook along a mountain path looking down into the valley. The story goes that it is a magical spot and if you shout out your question across the valley your fortune will echo back to you and your future will be told.
Fischer tells Chirac and Bush the story and they all decide that in the best interests of their countries they will go to the valley overlook and have their countries’ futures and fortunes predicted. They all bundle up and walk along the precarious alpen path to the magical overlook…
Fischer goes first and leans out over the edge and yells out his question.
"Vat iss ze future prosperity of Deutschland???
A few seconds later from across the valley echoes the reply and fortune…
LAND…LAND…LAND…LAND…LAND
Fischer says,“Ziss is very good, my country vill be endowed with more land!”
Chirac goes next and leans out over the edge and shouts out his question.
"Ouat is the future prosperite’ of Frankreich??? (Frankreich=France)
A few seconds later from across the valley echoes the reply and fortune…
REICH…REICH…REICH…REICH…REICH (Reich=Rich)
Chirac says, “C’est bon, my country will become very rich!”
Last up, Bush finally leans out over the edge and shouts his question across the valley.
"What is the future prosperity of The United States???
A few seconds later from across the valley echoes the reply and fortune…
AIDS…AIDS…AIDS…AIDS…AIDS
…
(I didn’t write the joke…I’m just telling it ::Ducks the flying fruit:
Oooh, I found an excellent example of German humor.
A boardgame called Drunter and Druber. Its a tile laying game where players vote whenever they want to demolish a toilet. 
I love that game.
Okay, that’s pretty damn funny once I know what the sign says.
A current bit of german street humor: Planting the W flag on Mt. Doo
If it involves piss, it is funny in any language.
Speaking of piss:
When we were at quite a rowdy party on our last weekend in Germany, my husband pulled my into the men’s room to show me something that had him giggling.
In the urinal, down by the drain was a minature soccer goal with a little ball in there to help make the guys practice aiming. And y’know what, there wasn’t a drop on the floor. Which if you saw how they were all drinking…it was nothing short of a miracle.
I shoulda, but didn’t, take a picture of it.
A friend of mine in college had a German boyfriend. Both my friend and I spoke German (me passably, she quite well), so he told us a joke in German. It went something like this:
So, the neo-Nazi stops a Jewish man on the street and says, “Is this the way to Aldi?” The Jew says “To.” The Nazi says, “Oh, I thought they were still open.”
No one got it.
The poor boyfriend had to carefully explain the whole thing to us at great length. First, Aldi is a chain of German discount grocery stores. Secondly, the joke is a pun based on a sticky point of German grammar. There are two ways to say “to” when you’re talking about going somewhere, “nach” and “zu”. It depends on what kind of place you’re going to. (That’s why the joke makes no sense even to people who understand German unless they also know what kind of place “Aldi” is.) In the joke in German, the Nazi used the incorrect form of “to” for that sentence (“nach”). The Jew corrected him, but the other word for “to” (“zu”) also sounds like a way to say “It’s closed.”
My friend was still confused, though. “Why was the guy a Nazi, though? What did that have to do with anything?” Her boyfriend said, “It just means that he is stupid! His grammar is wrong! The Jew speaks better German than him, but the Nazi is so stupid he doesn’t even understand what he is saying!”
Now that is the part I thought was really funny. Once I understood the joke it was obvious that it was of the familiar “Stupid person says something wrong, then comically misunderstands correction” type. In the US, it might be told as a Polish joke. But modern Germans can’t make jokes about the Polish! They can’t in good conscience make ethnic jokes at all! They’ve got to recast them as stupid Nazi jokes!
As a postscript, I’ll mention that I actually lived out a form of this joke while in Germany. I asked a bus driver in Weimar, “Fahren Sie nach XYZstrasse?” He said “zu”. I blinked at him for a moment, wondering why the street was closed, until I realized that he was correcting my grammar.
I work with a bunch of Germans and they all seem to get a kick out of any joke involving any other nationality, especially the “Island Monkeys” (British). Also they laugh like hell when you substitute the word idiot with American in any conversation. And jokes…The more vulgar, the better.
I heard this one in my high school German class. It’s really dumb.
Eine bayerische Frau sagt zu Kasimir, „Küss mir, Kasimir!”
Kasimir behebt sie: „Nicht mir; mich!”
Die bayerische Frau sagt, „Küss mir, Kasimich!”
[sub]It was explained that sometimes Bavarians use ‘mir’ where ‘mich’ should be used.[/sub]
Actually they have many Jokes of the Polish variety, the culture that has earned “Polish status” and is the traditional brunt of this humor are German Ost Frieslanders(East Friesland)
“I just finished training my infant to shit on command, and boy, are my arms tired.”
FWIW, I liked the joke about the Indian doctor the most.
My best friend is German and has a great sense of humor, and has no problems understanding mine, no matter the subject.
The funniest thing he said recently was in reaction to an accident my aunt had; she’d gotten hit by a golf cart and the driver never saw her, never heard her shouting for him to stop when her coat caught under the wheel, and never stopped, essentially running her over.
Me: “She is a big woman, and it was a golf cart, I don’t see how he could have missed her!”
Him: “Well, he didn’t.”
If you go by my husband, you will know that there IS no German humor. You can laugh at them, but not with them. 
The toiletpaper joke makes sense to me, but I don’t find it that funny. My understanding of it:
-Stealing toilet-paper is ridiculous.
-Putting so much thought into a method to steal it is more ridiculous.
-Getting five years in prison for it is completely absurd.
-Yet with all that, the guy at the end acts as if the events described were not only reasonable, but the only reasonable way for events to unfold. That’s the silly part.
Maybe it’s better told out loud.
Daniel
I think “Polish jokes” are probably universal, it’s just a matter of which group is standing in for the Polish. It was just funny for me to realize that a modern German might feel pretty bad about making “Polish jokes” about the actual Polish.
My friend’s boyfriend may have been a bit more sensitive than most, though. I remember he was shocked by her casual use of the word “ghetto” to describe things of poor quality (she’s African-American). She had to explain to him that she didn’t mean that kind of ghetto.
Okay, here is German humor. And it doesn’t even get lost in the translation, although knowing it makes it even funnier.
Click on “Clip ansehen” under “Brad & Pitt” then click in one of the three circles to choose your speed and then click “Speichern und zum Video”. Hint, the guys are named Brad and Pitt.
Even funnier, if you do know the language:
(The joke is that in the end one says: “Damn! We were lucky!” And the other: “Yeah, he didn’t see us.”)
Or just view them at leisure. Courtesy of my German Friend.
I can recommend a German novel that I think is utterly hilarious: With The Next Man Everything Will Be Different, by Eva Heller.
It’s about a 27y/o female grad student in Berlin, 1987. It’s a satire, but not as broad as it might be: much of the humor is in how situations play out, not merely the presentation. At the start of the book, Constance breaks up with her live-in boyfriend, and spends the rest of the story searching for that next man while planning to make THE!!! student film that will revolutionize cinema.
Not to be confused with Bridget Jones, Constance is a wannabe intellectual who hopes to someday be liberated and married at the same time. She’s pretentious, rather than discombobulated, and a keen observer, though she doesn’t always draw the same conclusions as the reader. The supporting characters are well fleshed out, and there’s a lot of social commentary.
And it’s funny, is my point. Not slapstick, but “Omigod, I know people just like that” funny. If you read it, you should be hooked by the birthday party scene. “It was as casual as a dentist’s waiting room.”
The American version ends thusly:
So the Texan thinks for a second, and says, “All right, then. Can you tell me where Faneuil Hall is at, asshole?”
I find that joke funny, Not absolutely hilarious…but it is funny.
{I’m half German :D}