Did a test series comparing depth of field at various apertures on a DSLR and a point-and-shoot. DOF varies by focal length, aperture, and distance. Subject distance was held relatively constant throughout and I tried to give equivalent fields of view for the shots. I was handholding though, so they aren't perfect.
The DSLR was a Nikon D700 with a 24-70 f/2.8 zoom lens. The point-and-shoot was a Leica D-Lux 4. All shots taken in aperture priority mode (obviously). Since the purpose of this test relates to DOF, no effort was made to hold white balance constant or even exposure constant. Whatever the camera meters said was right is what I shot. All shots are JPEGs right off the memory cards without any tweaking done in Aperture.
First the DSLR shots:
Nikon D700 f/2.8 60mm
Nikon D700 f/4 58mm (got a little zoom creep in this series)
Nikon D700 f/5.6 58mm
Nikon D700 f/8 58mm
Nikon D700 f/11 56mm (more zoom creep)
Nikon D700 f/16 56mm
Nikon D700 f/22 56mm
Now the point-and-shoot:
Leica D-Lux 4 f/2.8 12.8mm (but similar field of view to 60mm in 35mm terms)
Leica D-Lux 4 f/4 12.8mm
Leica D-Lux 4 f/5.6 12.8mm
Leica D-Lux 4 f/8 12.8mm
Even though the field of views are roughly similar throughout, the focal lengths needed to produce them aren't. 60mm on a full frame body is close to 12.8mm on a point-and-shoot. So even wide open at f/2.8 the Leica has a fairly large DOF (to my eyes equal to about f/11 on the Nikon). Because of their tiny focal lengths, it is impossible to "blur out the background" with point-and-shoots even at large apertures. The only way point-and-shoots can isolate a subject is in macro mode with VERY close subjects. At very short subject distances, DOF shrinks rapidly even with small apertures.
The DSLR was a Nikon D700 with a 24-70 f/2.8 zoom lens. The point-and-shoot was a Leica D-Lux 4. All shots taken in aperture priority mode (obviously). Since the purpose of this test relates to DOF, no effort was made to hold white balance constant or even exposure constant. Whatever the camera meters said was right is what I shot. All shots are JPEGs right off the memory cards without any tweaking done in Aperture.
First the DSLR shots:

Nikon D700 f/2.8 60mm

Nikon D700 f/4 58mm (got a little zoom creep in this series)

Nikon D700 f/5.6 58mm

Nikon D700 f/8 58mm

Nikon D700 f/11 56mm (more zoom creep)

Nikon D700 f/16 56mm

Nikon D700 f/22 56mm
Now the point-and-shoot:

Leica D-Lux 4 f/2.8 12.8mm (but similar field of view to 60mm in 35mm terms)

Leica D-Lux 4 f/4 12.8mm

Leica D-Lux 4 f/5.6 12.8mm

Leica D-Lux 4 f/8 12.8mm
Even though the field of views are roughly similar throughout, the focal lengths needed to produce them aren't. 60mm on a full frame body is close to 12.8mm on a point-and-shoot. So even wide open at f/2.8 the Leica has a fairly large DOF (to my eyes equal to about f/11 on the Nikon). Because of their tiny focal lengths, it is impossible to "blur out the background" with point-and-shoots even at large apertures. The only way point-and-shoots can isolate a subject is in macro mode with VERY close subjects. At very short subject distances, DOF shrinks rapidly even with small apertures.