Is the rear wheel up and down movement, or if you grab the top and bottom of the wheel, can you rock it by pushing in on top and out on the bottom, then vise versa? If the latter, then it's a loose axle nut.
On the front, hold on to the backing plate, and rock the wheel. If the backing plate doesn't move, but the wheel does, then it's loose wheel bearings. If they both rock together, then it's kingpins