One of the most famous performers was Scott Joplin, who published the 'Maple Leaf Rag' in 1899; this heavily influenced subsequent pieces. It was also Joplin who composed 'The Entertainer', a piece still popular today. Claude Debussy was also very influenced by ragtime pieces.
On a more personal note, I love playing ragtime music as it's really fun and cheery to play! At one point, I would constantly play just a few bars of one piece in BTEC Music, and would be yelled at to stop- though at least one person was guilty of humming it after. Unfortunately I couldn't find that piece on Grooveshark :(
Maple Leaf Rag- Scott Joplin
The Entertainer- Scott Joplin
Le Petit Negre- Claude Debussy