I have always said it like 'io-deen' because whenever 'ine' is used (eg. amine, or fluorine) it is said that way. Sometimes I'm corrected by people who think it should be pronounced 'io-dyne', which is correct?
Manshu is correct,in British English we pronounce iodine as in seen while in North American English we pronounce it as in mine.
Think about how other halogens are pronounced: fluor-een, chlor-een, brom-een, astat-een, and newly named tenness-een. Why would it be io-dyne and not iod-een?