I've heard that Tiro recorded three volumes of Cicero's jokes. Does any significant portion of these jokes remain? I don't seem to have been able to find a collection of Cicero's jokes on Google.
Tiro's books on Cicero's jokes are completely lost, and probably, if the opinion of ancient commentators is any indication, for the better. We know about them from Quintilian 6.3.5:
Vtinamque libertus eius Tiro, aut alius, quisquis fuit, qui tris hac de re libros edidit, parcius dictorum numero indulsissent et plus iudicii in eligendis quam in congerendis studii adhibuissent
And I wish that his freedman Tiro, or whoever it was who published three books on this matter [that is, jokes, which is what Quintilian's been talking about], had granted a fewer number of sayings [literally "had indulged in a fewer number," but I'm not sure how to do that in English] and shown more judgement in choosing than eagerness
Tiro's book may well have contained a great deal that wasn't by Cicero at all, and as we can see from Quintilian there was doubt even in antiquity that Tiro was the author at all. Collections of sayings like this were a relatively common publication--Augustus, according to Suetonius, wrote to Macer to prevent him from publishing a collection of Caesar's sayings--and just the way that lots of false quotations are attributed to people like Einstein or Mark Twain these days, lots of false attributions were flitting about Rome. Cicero, being the great orator and writer of his time, was a particular target for these false attributions. Already in his own lifetime he complained about false quotations of his floating around. In a letter in 50, he said:
ais enim, ut ego discesserim, omnia omnium dicta, in iis etiam Sestiana, in me conferri.
For you affirm that since I have departed every saying of everyone, even Sestius', are conferred on me
If Tiro was not in fact the author of this book then in all likelihood it probably contained a large number of spurious quotations. But even if Tiro was the author, Quintilian has a low opinion of the work and Cicero's humor in general, saying that Cicero was too ready to make a joke, which lessened the rhetorical effect of his humor. Cicero's speeches and letters are full of jokes, so we have a decent idea of the sort of thing that was in that book. On the whole, I agree with Quintilian--Cicero, while possessing an incomparable wit, was too quick to jest, and it fills a lot of his rhetoric up with obviously untrue accusations, particularly in speeches where he really doesn't have a leg to stand on