There was once a widespread rumor that Chao apparently couldn't reincarnate more than two times. It's possible for them to reincarnate potentially 255 times due to data limitations.
While it didn't directly spawn the once-common rumor of a "Sonic and Knuckles RPG", there was some speculation that said (ultimately theoretical) project had been retooled into this game.
Writer Revolt: The director of Sonic Adventure 2 was so angry at the negative reception for Big the Cat in the previous game that he took personal offense to it and put Big the Cat as a hidden secret in every stage as a spiteful act of vengeance towards everyone.
Originally the game was only going to feature Sonic, Knuckles, and Eggman as playable characters. The alternate stages would be branching, a feature that would return in Shadow the Hedgehog.
Shadow’s original name was “Terios”, which means “reflection of”, and Rouge’s original name was “Nails”.
Sonic was originally going to wear his sneakers from the Genesis games, instead of his SOAP shoes which enabled him to grind. The demo released along with Phantasy Star Online still has these shoes (likely before the endorsement deal had been fully inked).
Some leftover data from the Dreamcast version shows that originally the Black Market was going to be in Sonic Adventure 2, instead of Battle.
In addition, there was a Chao Playground and Chao Library planned. The Library would allow you to create new files for the Chao Adventure VMU game, but the Playground's function is unknown. Geometry data for them still exists in the PC version.
In Battle, after getting an A-Rank on Green Hill Zone, Super Shadow and Super Sonic would have been unlocked in two-player mode. All that exists are the unlock message and character select descriptions.
Apparently, Tails wasn't even going to be in the game, which would have been quite odd considering how he is known and loved by the fans as much as Sonic. Tails was thrown in at the last minute to be the counterpart to Dr. Eggman in gameplay.