A classical one is of course Norw. øye, Danish øje vs. French oeuil 'eye'.
Danish øj- is now [oj-], but my own grandfather actually had the ø-sound,
and apocope to boot, so that the result was exactly as in present-day
French. These are cognate of course, but only in the root part. Funnier is
perhaps Naukan Eskimo /eje/ (e = schwa) 'eye' from Proto-Esk. *ede (d =
"edh") and so totally unrelated to øje/oeuil.
Has somebody already mentioned Basque elkar and Dutch elkaar, both
meaning 'each other'?