Relative importance of research publications for grad school admissions (theoretical physics/pure mathematics)
The main thing that graduate school admissions committees are looking for are good researchers. Publishing papers demonstrates such ability; publishing papers in well-known journals is even better. However, it's difficult, as an undergraduate, to publish papers as first author (which is the most important position when one is applying as a student). Typically, they will be working in consultation with a more experienced student, who will be the lead author. In that case, while the credits are of themselves useful, they need to be coupled to strong letters of recommendation from the co-authors, testifying to the student's original efforts in executing the work.

At the same time, one should not totally sacrifice depth in a single area for breadth; grad schools want to see some evidence of concentration, but complete devotion to one area is also too much of an extreme. Try to balance the two somewhat, so that you've explored a few areas, and worked at least one or two areas in depth.