Well, you obviously cannot store the intermediate results in memory (unless you've got some sort of absurd computer at your disposal); you will have to write the results to disk.
The recursion depth isn't a result of the number of considered characters - its determined by what the maximum string length you're willing to consider.
For instance, my install of python 2.6.2 has it's default recursion limit set to 1000. Arguable, I should be able to generate all possible 1-1000 length strings given a character set within this limitation (now, I think the recursion limit applies to total stack depth, so the actual limit may be less than 1000).
Edit (added python sample):
The following python snippet will produce what you're asking for (limiting itself to the given runtime stack limits):
from string import ascii_lowercase
def generate(base="", charset=ascii_lowercase):
for c in charset:
next = base + c
yield next
try:
for s in generate(next, charset):
yield s
except:
continue
for s in generate():
print s
One could produce essentially the same in C# by try/catching on StackOverflowException. As I'm typing this update, the script is running, chewing up one of my cores. However, memory usage is constant at less than 7MB. Now, I'm only print to stdout since I'm not interested in capturing the result, but I think it proves the point above. ;)
Addendum to the example:
Interesting note: Looking closer at running processes, python is actually I/O bound with the above example. It's only using 7% of my CPU, while the rest of the core is bound rending the results in my command window. Minimizing the window allows python to climb to 40% of total CPU usage, this is on a 2 core machine.