Me and my brothers solved the game when we were little. We still play it sometimes since we forget how to win, but after a few games we end up solving it again. I’ve also hear other variations were you are allowed to say up to three numbers and with ending numbers higher than 21.

Here’s an example of how it goes:

Me: 1
You: 2,3
Me: 4,5
You: 6
Me: 7,8
You: 9,10
Me: 11
You: 12
Me: 13,14
You: 15,16
Me: 17
You: 18,19
Me: 20
You: 21 (lose)

It looks like 17 is a winning number. We worked our way backwards after that to solve it

You need a group of at least three people, but I’d strongly recommend at least five.
One goes away for a while (can’t hear), while the others settle on a rule for answering questions (this will be clear, I promise). For example, they accord on the rule of answering always naming some food.
The one asking questions comes back, and start asking whoever and whatever he/she wants to. He can ask how many questions as he wants (or maybe you should put a limit), and has three guesses to find the rule they are using.

Continuing with the food example rule, he could ask “How old are you?” and get the answer “I’ve seen 31 corn seasons already”, or “I have as many years as the eggs in the fridge”, or just “Hamburger!”.
There’s no obligation to give real answers to the questions, so there are many many possibilities.

Some nice examples:
Start with some letter (easy)
End with some letter (little harder)
Use the name of the one asking (easy)
Answer the question before yours (hard). I like this one, so I’ll put an example:
Q: How do you feel about this game?
A: I don’t know… (made up answer, since there’s no preceding question).

Q: Do you like cheese?
A: I think I’m having fun. (answers the previous Q)

Q: Is someone at the door?
A: Very much indeed.
… (and so on)

It seems easy for all who know the rule, but it’s intriguing for the one asking.

Oh, and I too play the car plates game (when someone humors me ^_^ ), it’s fun what you can come up with (since we have alphanumeric plates). But the first to say something wins (it has to be a proper sentence, no proper nouns, and, hopefully, funny).

By the way, I LOVE XKCD!!!
Keep it on!

Here (Argentina), we call “fantasma” (ghost) a different game, that also fills the requirements, is also a word game, and is fun. It’s like this:
Someone says a word to start a sentence. Eg. “I”.
The next player repeats the sentence that far and adds a word. Eg. “I like”
If you say a word that doesn’t seem to let the next player continue the sentence, you may get “challenged”, to show you can add some word (it’s really difficult to close a sentence for good, at least in spanish, but you can put them against a grammatic corner). The one being wrong looses.
If you make a mistake repeating the sentence (or pause for too long, or miss your turn), you loose.
If you are more than two players, you have extra rules (that actually name the game):
The first time you loose, you become “dead”, but keep playing normally.
The one to loose starts a new sentence.
The second time you loose, you become a “ghost” (or maybe a “phantom”, translation gets confusing there ), and can’t play anymore. But you have a new mission:
Ghosts try to distract players dead and alive by talking to them or making funny faces. Player can´t talk to or look at ghosts (they don’t exist, you know?), so if someone does he/she looses, and the ghost is real, so lives again.
You can keep points by counting looses, or play until there’s only one left alive, or not care about winning and loosing at all.
Hope you try and like…
I’m posting another one.