What is the PRG period of stream ciphers such as RC4 or Salsa20?
The internal state of RC4 consists of a shuffled 256-element array and two pointers into that array.  Thus, there are a total of $$256! \times 256^2 \approx 2^{1700.00}$$ possible states.  Since the state update function of RC4 is reversible, it acts as a permutation on this set of possible states, so that every starting state will eventually recur after sufficiently many iterations.

How many is sufficiently many?  Well, if we assume that the update function behaves like a random permutation (which it, of course, does not, but it's a good first approximation), then the expected cycle length is approximately $2^{1700}/2 = 2^{1699}$ iterations(!).  Indeed, the probability that the cycle length starting from a random state is at least $k$ iterations is approximately $1 - k/2^{1700}$; this means that hitting a cycle of less than, say, $2^{200}$ iterations should happen less than once in $2^{1700-200} = 2^{1500}$ initializations, i.e. basically never within the lifetime of the universe.

Of course, as noted, the RC4 state update function is not a random permutation.  For example, there's a known class of $254!$ short cycles of $256^2-256 = 65280$ states each; fortunately, the standard RC4 key setup is guaranteed never to hit them.  For more information on the actual cycle structure of RC4, see e.g. "Cryptanalysis of RC4-like Ciphers" by S. Mister and S. E. Tavares.