I like to point out that spreading this quote is an example of violating it: Buddha never said that. I'm not sure who did originally write it, but it's not found in any Buddhist primary source. "Do not believe in anything simply because it is spoken and rumored by many!"
I've heard it might be a rough paraphrase of a quote from the Kalama Sutta, but in its original form, it would not qualify as a "rationality quote"; it's more a defense of belief in belief, advising people to accept things as true based on whether believing it is true tends to increase one's happiness.
Edit: See RichardKennaway's reply; he is correct about this one. I think I was thinking of a different quote along similar lines.
it's not found in any Buddhist primary source
What is a Buddhist primary source? None of the discourses were written down until some centuries after the Buddha's time. The discourses that we have do themselves exist and whatever their provenance before the earliest extant documents, they are part of the canon of Buddhism. The canon has accreted layers over the centuries, but the Kalama Sutta is part of the earliest layer, the Tripitaka.
I've heard it might be
You've heard? That it might be? :-)
It is readily available online in English translation. It...
This is our monthly thread for collecting these little gems and pearls of wisdom, rationality-related quotes you've seen recently, or had stored in your quotesfile for ages, and which might be handy to link to in one of our discussions.