Just for fun, here's an even simpler design. This was reverse engineered from someone else's design, and I must admit that I can't for the life of me figure out a reasonably simple formula for how to choose resistor values - it's a combination of experience, luck, and simulations. It doesn't have as crisp of a limit as the others, but it works fairly well with even fewer components.

I've included a version @crutschow's circuit at the top, and two variations of the borrowed circuit below it. I think Crutschow's performs a little better, and is much easier to setup, so it would be my go-to in most situations, but the tinkerer in me is fascinated by the mechanisms of the simpler circuit, and if you were really trying to pinch pennies on a high-volume design, the reduced parts count might be useful.
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After posting these earlier, I did a little more poking around, trying to understand them better, and I think I'm finally starting to get it. Unfortunately, if my understanding is correct, the performance is highly dependent on transistor beta, which would give this circuit very wide tolerances on output current, good for stopping dead shorts, but not very good at "regulating" anything.

***EDIT: Just to be clear, the comments above are referring to the single-transistor circuits I recently posted, not the circuits from Crutschow and Bordodynov. I have complete faith in the circuits each of them shared.

 

if my understanding is correct, the performance is highly dependent on transistor beta,

Yes, I believe that's true.
So to get a particular current limit in the real circuit you would likely have to select a least one of the resistor values at test or use a pot.