In Pokémon Gold and Silver there are a few Egg moves which are impossible to learn or are redundant due to already being passed down via a TM. This Egg move data was removed in Pokémon Crystal.
The unused Egg moves were documented on Japanese Pokémon Wiki and IIMarckus in the English Pokémon glitch community.
Charm on Oddish
In Pokémon Gold and Silver, Oddish has Charm as an Egg move but there are no legitimate fathers in Oddish's Egg group Grass who learn the move to pass it down. (source)
Lovely Kiss on Smoochum
Smoochum has Lovely Kiss as an Egg move, but since Jynx (the only Pokémon from the Human-Like Egg group to learn Lovely Kiss) is a female-only species it cannot pass down the move. (source)
Staryu's Egg moves
Staryu has Egg moves for Aurora Beam, Barrier, and Supersonic but cannot learn them as it is genderless and can only breed with Ditto.
Redundant Egg moves
Several Pokémon[clarification needed] have Egg moves Steel Wing and Sweet Scent. However, since these are TMs they are passed down anyway.