I'd like to create a hollow tube by sweeping along a curve. I create the curve and two concentric circles. I sweep one circle, and then the other, along the curve, but I just end up with a solid tube the diameter of the larger circle. What am I doing wrong?

Nothing is wrong but you have not finished the work! ;)

Select the Big Cylinder Volume
Construct / Boolean Diff and Click the Internal Cylinder)
Et voilà!




For Pipes you can use some Plugins
http://kyticka.webzdarma.cz/3d/moi/#Pipe

Aah, I see. Thanks.