This came up in another thread and I could see the debate start to get things off topic so here we are in it's own thread now.
Yes sensor size does effect DOF (Depth of Field) or how much of a picture is in focus. A point & shoot camera will have more of the picture (subject and background) in focus even if you use a low f number like f2.8. A larger sensor will give you less of the picture (shallow DOF) at f2.8. That's why medium format cameras can give you amazingly shallow DOF for isolating the subject from the background.
Now depending on how you measure it, DOF can change when comparing an FX camera and a DX camera. However a 50mm lens is still a 50mm lens regardless of whether it is FX or DX. With a DX lens you just get less of the image.
My original statement regarding DOF was in regards to using the SAME camera body and only switching from FX lenses to DX. All things being the same would mean the same DOF. You wouldn't get medium format like DOF if you could for example mount a medium format lens to a D90. So putting an FX lens on a D90 will not change your DOF.
So let the crazy math calculating begin!