The current limit for the base current of the second transistor is that transitor itself. The voltage drop over a conducting Base-Emitter junction is a fairly constant 0.6V. The drop over a conducting Collector-Emitter path can be much lower, down to maybe 0.2V. Hence the second transistor 'pinches' its own base current down by sinking current that lowers the voltage on its collector (and hence the ability of the first transistor to deliver base current).
This is one of the disadvantages of a standard darlington: you can't saturate it (overdrive the base to achive a very low Vce).
This of course assumes that there is some load in the collector line that drops more voltage when the current increases. But if there isn't the collector current isn't limited, so we would be in deep shit anyway.
A transistor is always some what leaky. Without R2 the leakage current of the first transistor would be amplifier by the second one, so it would always be slightly on. Another purpose of R2 is to make the second transistor switch off faster: it quickly removes the remaining charge on the base after the first transistor has switched off.
I am not sure what R1 is for, but it is convenient when the darlington is driven from an output who's 0-level is somewhat above 0V, as could be the case with a loaded TTL output.