In order to model a part of a wire puzzle, I used a cylinder unit, added an array modifier to make it as long as I want, and finally added a curve modifier to give it its shape. To make it look nice, I wanted to add a subsurf modifier, but this resulted in a strange pattern that I do not understand - I expected just a smooth tubular shape as a result.
Can anyone explain where this is coming from, and how to avoid it? (I hope there is a solution that does not involve applying the modifiers.)
Your source mesh has front and back capping faces, deleting those gets rid of the seams:
However, there's a better way to build this shape. Get rid of the cylinder, and add a bezier or nurbs circle. On the path (not the circle) go down to bevel object, and select the circle from the dropdown, and also check "fill caps"
Not only do you not need to worry about open ends of the path vs seams, but you have total control over the polygon count of the resulting shape. The "resolution" setting on the path controls divisions along the length of the path, and the "resolution" setting on the circle controls the divisions around the tube.
