I was just thinking about what games I can recall that split a fanbase of an established franchise. Here's what came to mind:

Burnout Paradise: There seems to be a major divide between those who loved the streamlined experience of Burnout 3 and those who appreciate the open world and online innovations of Paradise

Grand Theft Auto IV: The GTA 3 trilogy was one of the most acclaimed game series of last gen. GTA IV has become one of the most acclaimed games of this gen, but is also faces one of the most prolific fanbase splits. Some loved how ridiculous the series got by San Andreas, others praise the more serious nature of GTA IV.

Halo 2: Many were dissapointed by how the storyline went down, while others were too distracted by the multiplayer that set the modern standard for console online multiplayer. 

Resident Evil 4: For many, 2005's game of the year came less than 2 weeks into the year. This highly influencial game reset the series gameplay with a new over the shoulder aiming mechanic and a higher focus on action rather than adventure. Some longtime franchise fans resented that change.

Every Console Zelda Game Following OoT: If there is one thing that just about every Zelda fan can agree with, it's that Ocarina of Time was an exceptional entry in the series and a landmark moment for video games. The 3 major sequels that followed it then provided some noticable cracks in the fanbase. People seem to either love or hate Majoras Mask. Wind Wakers cel-shaded art style provided a new aspect of the series to debate. Most recently, Twilight Princess has created an entirely new split between those who dug the fan service experience it strived for while others were turned off by how similiar it is to OoT and the tacked on motion controls the Wii version included.

Other Ones

Sonic Adventure
Prince of Persia: Warrior Within
Jak II
Street Fighter 3
Guitar Hero 3
Banjo-Kazooie: Nuts and Bolts
Metal Gear Solid 2
Colin McRae Dirt
Call of Duty World at War
Rainbow Six Lockdown
Left 4 Dead 2
Deus Ex: Invisible War
SW Knights of the Old Republic 2
Super Mario Sunshine
World of Warcraft
Final Fantasy XI and XIV
Fallout 3