We can see these circles in 3-space via stereographic projection. The image you see in the background of this web page is a picture of stereographically projected fibers corresponding to a circular path of base points on S2. Each fiber is linked with every other fiber. Since the Hopf map is surjective, stereographic projections of the set of all fibers fill all of 3-space with disjoint, linked circles (and one straight line, which is the fiber which passes through the point of projection).
This image is the product of an animated 3D imaging project by David Lyons (Mathematics), Paul Hemler (Computer Science) and Keeley Chorn (student) of Wake Forest University.
The paper referenced below is an account of geometric and algebraic topics surrounding the Hopf fibration for an undergraduate audience. I will send hard copies on request.
An Elementary Introduction to the Hopf Fibration, Mathematics Magazine 76(2): 87--98, 2003