Why aren't the normal titans affected by the 13-year curse? In Attack on Titan, the titans wandering around the walls seem to live longer than 13 years, bypassing the curse. We know for sure that the normal titans live longer because of the Smiling Titan.

But why aren't the wandering titans affected by the curse? Shouldn't all the titans have died just because of this curse?
The following answer contains spoilers from chapter 88 and after. (For those who don't read the manga: it's WAY beyond the anime)

As we know from chapter 88 


  among the "subjects of Ymir" there are always up to 9 people who inherit the power of the titans, a piece of Ymir's "soul" or power, which allows them to transform into one of the nine "special" titans. Along with this power they inherit the curse of Ymir, which is the reason they die 13 years after awakening to their powers.


On the other hand the "normal" titans were originally 


  "subjects of Ymir" who were transformed into titans by injecting titan spinal fluid into them. But they did not inherit the original titan power, so they didn't inherit the curse either.