No one has mentioned the Wii Sports/Play/Music/Fit series, which is quite surprising, though they aren't my pick.
For at least some series, you can argue that an overhaul is needed more than an execution. Longrunning series that have made efforts in the past to mix things up (e.g. Need for Speed, Call of Duty) can be defended by arguing that an overhaul is better than the guillotine. But if a series is story-based (like Halo or Gears of War), it should continue for only as long as the story continues. Otherwise, you're just pandering to the fans.
But if I had to axe a franchise, it might be Gran Turismo, for its sheer denial of the fact that there is a popular, accessible racing sim out there (Forza Motorsport) that has better game design. Maybe GT5 can change my mind, but it's too early to tell.