What is the complexity of rectangle packing when rotations are allowed?
We can reduce the no-rotations packing problem to the rotations-allowed packing problem as follows.  Take any instance $(R, r_1, r_2, \dots, r_n)$ of the no-rotation problem.  Vertically scale the entire instance by twice the ratio of the smallest width of any rectangle $r_i$ divided by the height of the container rectangle $R$.  (This ratio has a polynomial number of bits, so the transformation can be executed in polynomial time.)  Each scaled rectangle $r'\!\!_i$ fits inside the scaled container $R'$ only in its original orientation, so allowing rotations adds no new solutions.