There's only a choice of one axis - around which to deform. Ideally there'd be two (which to deform as well). Alas, there isn't. A way around that is to use an origin object (i.e. an Empty) and rotate it accordingly (in this case - either +90 or -90 around Y axis).

I'm not sure I understand what you mean by only being one choice. It gives the options of X, Y, and Z.

Yes, I could and I have. The screenshots and description explain how to create the problem. Do I need to attach the actual blend file with it already set up?

@Todd Gillissie (Gillissie) the modifier deforms geometry along an axis (1) around another axis (2). UI only allows you to choose (2), but not (1). In different software it's done differently. In Maya you freely transform the deformer; in Max you have more settings in the modifier. Blender, for whatever reason, has a mix of both: you have limited options via modifier parameters, and the additional options (center of deformation and axis) are done via Origin Object.

@Germano Cavalcante (mano-wii):

I'm sorry, but this is not clear nor intuitive at all. Why wouldn't it just work around the chosen axis without the need for another object? After all, the modifier is named "simple deform", not "complicated deform". :)

It does exactly that: "just" works around the chosen axis. No questions asked. One of those questions, if asked, would've been "what do you actually want to deform?". Because you may want to bend X around Y or Z around Y. The only way to "set" that in Blender is to use Origin Object and orient it appropriately. The alternative could've been a second dropdown in the UI, which would've been of course simpler than setting up a whole object, but you still need to set it.

This is overly complicated. There shouldn't be a need for a second factor. Only a single axis should be necessary to do what someone wants:

• Choosing X with 360 degrees of bend should form a circle around the X axis.
• Choosing Y with 360 degrees of bend should form a circle around the Y axis.
• Choosing Z with 360 degrees of bend should form a circle around the Z axis.

Can you give me examples of what you mean by "X around Y" and "Z around Y" ?

Upon further thought, I think I know what you mean by "X around Y", etc...
This makes me think that the UI should have two dropdowns instead of the need to make an object and transform it.
"Bend [X/Y/Z] axis around the [X/Y/Z] axis."

That's what I said in the very first reply, sorry if it wasn't clear.

Thanks for all the responses... eventually it became clear. I'm hoping that this could be addressed in the UI by simply adding the extra dropdown instead of the object picker.

This UI is a problematic one. Many others have reported here and I was about the do so.
Having the second origin to be as an empty gives the advantage of creating more interesting results (but makes the UI difficult to understand)

I think there should be a video demo and better documentation from the Blender.org explaining the features as most tutorials and the current documentation doesn't make it clear enough.