Couple more examples:
Mati meaning “eye” in Modern Greek, and mata meaning “eye” Malay. This one shows up in historical linguistics textbooks, copied from Bloomfield: Language.
One of the nicest counterexamples is meli meaning honey in Greek and Hawaiian. Nice, because it actually *is* a result of language contact (in a roundabout way): meli – Wiktionary (and it tripped up Trask in his textbook: Trask’s Historical Linguistics )
[Originally posted on http://quora.com/Are-there-words-in-two-different-languages-that-are-identical-by-coincidence-and-not-language-exposure-I-read-about-an-Aboriginal-language-that-used-dog-to-refer-to-a-dog-Are-there-two-words-that-sound-the-same-but-have-different-meanings/answer/Nick-Nicholas-5]