Auto Bezier-Curve option?

…t's hard to imagine how you envision this auto-curving feature actually working…

No it's not. Such features are quite commonplace. They appear in everything from the cheesy drawing modules of office applications to full-blown drawing programs including FreeHand, Corel Draw, ADC Canvas, and others. Inkscape has a particularly innovative (and quite useful) Spiro curve features which enables you to automatically constrain all curves to circular arcs.

How much curvature? In which direction(s)? The input to those variables comes when you manually drag out the handles.

"Dragging handles out of an anchor point" is just the defacto standard interface convention for drawing cubic Bezier curves. A cubic Bezier curve consists of four coordinate pairs in  a sequential order. There is no actual "connection" between the two middle off-path points and the two on-path points (what we call "handles"). That's all just interface smoke-and-mirrors to make an intuitive interface. But there's nothing preventing a different interface.

Such features as PMearns has in mind are usually associated with creating quadratic Bezier curves (which have one off-path point per segment) instead of cubic (which have two per segment). The first click positions the first on-path point. The second click positions the off-path point. The third click positions the second on-path point (ending the current segment and starting the next), and so on. The curve is plotted between them, influenced by the sequence of off-path. (The quadratic curves are usually converted to cubic when exported.) Illustrator doesn't provide for drawing quadratic Beziers or other kinds of splines.

…does the pen tool have some sort of option to automatically curve the lines made when clicking from point to point?…an option to automatically create curves without manually dragging out bezier handles?

Not so far as version CS6. I don't rent software, so I don't really keep up with what's been added to CC versions.

Is there also a shortcut to stop an auto-bezier with the next anchor point, or can that only be done by clicking on the last anchor point made?

In Illustrator, while drawing with the Pen, tapping Enter will end the current path. The next mousedown with the Pen will begin a new path.

JET

Assuming I understand the question, it's hard to imagine how you envision this auto-curving feature actually working.

PMearns  wrote ...to automatically create curves without manually dragging out bezier handles?

How much curvature? In which direction(s)? The input to those variables comes when you manually drag out the handles. How would an automatic curve feature acquire, process, and execute the properties of your desired curve "automatically?"

Is there also a shortcut to stop an auto-bezier with the next anchor point, or can that only be done by clicking on the last anchor point made?

What's an "auto-bezier"?