Under the "Extra Stuff" tab I found three characters that existed in earlier drafts but never made it to the final book:
In the second book the Weasley's make a reference to a second cousin who is a stockbroker. Mafalda was going to be the daughter of that second cousin. In one version of the fourth book, she was sent to stay the summer with the Weasley's where they find her to be the most horrible girl ever. Smart like Hermione, enough to make her jealous, but rude. She was to be sorted into Slytherin house and since she is very nosy and can't keep her mouth shut, Harry would learn a lot about the Death Eaters from her character. She was eventually cut and the character of Rita Skeeter was built up to serve the same function.
Another cut character from the fourth book was Mopsy, a batty old dog-lover living just outside of Hogsmeade. Originally she had taken Sirius in, thinking he was just a stray. She was fun and eccentric, but essentially unimportant... and it became too difficult for Harry, Ron, and Hermione to ever speak with Sirius. The story was changed to where Sirius stayed hidden in a cave, and not with Mopsy.
There were many rewrites of the first chapter of the first book, and one involved Pyrites (meaning "Fool's Gold") who was a servant of Voldemort's. He was a "dandy" as Rowling puts it and always wore white gloves. In the scene he was meeting with Sirius, but that whole idea was scratched including his entire character.