Well, here's an example from the lojban translation of Alice in Wonderland:
i lu mi’a te cmene ra lu ractu cafmi’a li’u ki’u le nu ra ctuca mi’a sei la
jitfa cakyrespa cu fengu cusku
This is the equivalent of the English version:
`We called him Tortoise because he taught us,' said the Mock Turtle angrily.
The English translation of the lojban is:
"We called him 'lapine frequent-laugher' beacause he taught us," said the Mock Turtle angrily.
Where it is playing on the similarity in sound between "ractu cafmi'a" and "ra ctuca mi'a"
Now, admittedly, my puns tend to be cross-language puns, such as this one:
Q: paunai mu'i ma lo lojbo bebna cu fengu fi lo du'u lo me la'o donut dunkin munchkin donut tanxe cu vasru xano po'o titnanba
A: mu'i lo nu lo tanxe cu se tcita lu bitesize li'u
("Why was the lojbannic fool angry that the box of "Dunkin' Munchkins" only had 60 pastries?" "Because the box said 'bitesize'[which reads to a lojbanist as "87"])
Or this one: [Snick, close your eyes NOW]
Q: ma krinu le za'i no lo tigni be lo nu cinse cu speni
A: .i ty du single
"Why are no sex entertainers married?" "Because they are stage-screwers"
(playing on the similarity to the lojban word "single" (which would read to a lojbanist as a short form of "tsina gletu" (stage/platform+to perform a sex act)) to the English word)[okay, Snick, you can open them again]
Of course, there are also lots of other types of wordplay, such as palindromes, tongue-twisters and and pangrams.