At the risk of seeming fawning I'm going to praise something of Zak's again. The goblins that show up in episode 8 of I Hit it With My Axe always say the opposite of what they mean. In trying to communicate with these goblins the player characters have to do the same. And what happens (if you don't have time to watch and see) is that the players immediately perk up, everyone is attentive of what's going on, they're puzzled for a second, have a flash as they realize what's going on, and then they all start contributing their own opposite talk.
I think that's great. That's the whole point of this game right-- everyone involved, laughing and creating together? What makes this achievement especially cool is that (if I'm remembering correctly) at least some of these players were leery of having to create on the spot at the game table-- and here they were creating willingly and successfully. After seeing that episode (and a few after it) I've been wracking my brains trying to think of equally simple ways to pull players in.
You might consider these the smallest possible of games within a game, and if they work the same way as the goblin opposite talk, they'll be fun not just because they draw players into the game creatively but because they highlight the ironic distance of players trying to be successful dungeoneers by making up the best silly sentences.
I've got some ideas in several categories so I thought I'd break them up into several posts. Let's start with:
You can't use a certain vowel. In English the frequency of vowels is e a o i u y. I might stick to the middle three as a balance between being too hard and being frequent enough to actually make the players have to stop and think. So, maybe the a local dialect of Thieves' Cant is just Common with no "a"s, that's how the thieves know who is in the the "know."
"Oi, governor, the shipment comes in the first night of this week. We'll pick it up before you might wink your pretty eyes."
You have to start all your words with the same sound (you might forgive prepositions and articles and such). This might be the way to activate a particular magic item.
"Bring back blessed brother Boniface!"
It varies by what corpus you look at but the frequency of consonants in the initial letter of English words is something like t s h w b m f c l d p n g r k j v q z x. This means you could vary the difficulty to use and power of the above magic item by requiring "t"s for the very easy to "r"s for much harder.
Any gibberish language games might work as long as they're consistent and simple-- Pig Latin, Double Dutch, etc. Of course it would work best if some of your players new one of these already. Most of these are easily understood by a listener unless they are used so sparingly as to hide the pattern or rattled off quickly enough to do the same. Maybe the test is if you as DM can follow so can the npcs.
"This wine is the best in the city!"
"Gentlemen, I understand your gibberish"
Rhyming in English is hard. I wouldn't recommend this as a mini game but if you're playing in a different language it might work great. It could work if the rhymed words didn't have to make literal sense, like Cockney Rhyming slang or a code or something, but that is more of a word constraint. I'll cover some of those next post.