How many recursive md5 hashes are needed to always get same string
After about $2^{n/2}=2^{64}$ iterations an input will enter a cycle (of length approximately $2^{n/2}=2^{64}$). If inputs didn't collide by the time they enter a cycle, they never will.

If you have more than about $2^{n/4}=2^{32}$ inputs, you'll get collisions after $2^{n/2}=2^{64}$ iterations, as per birthday-problem. But of course you won't have the patience to wait that long.