These VR images are usually shot with standard camera as a multi image panorama, and then processed in software.

The easiest way is to use a special panoramic (sometimes called VR) tripod head which pivots the camera about the exact centre of the lens in order to ensure the photos line up and there's no paralax error. Shooting vertically with a wide angle lens, ideally a 20mm equiv. or wider, pan through 360 degrees, then take the camera off the tripod and shoot a single sky and ground image (i.e. straight up and straight down)

If you don't have a wide lens you can shoot a two or three row panorama. This can avoid the need for a sky/ground shot, but you'll have tripod legs in your ground shot! There's no need to use a fisheye lens, a standard rectiliear lens will do, the software will do the rest.

The images need to be assembled using a special piece of software which will stitch the images together to create a single 360 degree by 180 degree rectangular image, or a cube map if you prefer. PTGui is often recommended for this task. Other good panorama stitching programs should be able to do this as well.

There's obviously quite a bit of post processing involved, but if you shoot with a good overlap between images the software should be able to assemble them with little interaction, though it might take a while to process.

Shooting multiple exposures in each position and creating a tonemapped HDR panorama is also commonly done, as it helps deal with large changes in brightness you can get planning through 360 degrees, especially outdoors in direct sunlight.