Not really. There are franchises that I follow and will continue to do so as long as they entertain me. They would include: Command and Conquer, Dawn of War, Mass Effect, Halo, Unreal, Gears of War, Quake, Doom, Age of Empires (don't think I'll be getting another one any time soon), Half-Life and a few others.
There have been franchises that spurned me: Quake (quake 4 was a terrible mashup of quake 2 and quake 3 being run on the Doom 3 engine (the engine incidentally can render lights, contrary to popular belief) leading to a very muddled and inconsistent game experience), Call of Duty (Modern Warfare 2 can die in a god-damn fire. No game has ever managed to consistently frustrate me to the point of anger except MW2), Zelda (After Ocarina of Time, the franchise has basically become a rinse and repeat sort of thing. A few more identical entries meant that it would take nothing short of a miracle to get me excited about a Zelda game again), and anything with Alien vs. Predator in the title. The 1999 entry from Rebellion was one of the great shooters of the era. The sequel was even better with the addition of useful multiplayer functionality (I seem to recall the first game supported direct IP address entry (no browser at all) and mplayer.com functionality). Then, there were a few terrible console games and movies that were even worse followed by a better looking version of the 1999 game that actually played worse in most respects.