Depending on how much you're willing to look into it, kinda? In The Amazing Spider-Man, Peter catches a fly (0'15 in the clip below), and is seen licking his fingers at 0'30. Might not be actual craving though, perhaps just uneasiness.
In Spider-Man: The Animated Series Spider-Man mutates into his final mutation form from the initial spider bite and becomes Man-Spider. Presumably he ate some bugs in this form even if we don’t explicitly see it, that I remember.