The first mirrorless camera models from Panasonic and Olympus, dubbed Micro Four Thirds, featured standard 17.3x13.0mm Four Thirds sensors, the same sensors as those used in Olympus' larger DSLRs (the "Micro" refers to the body design, not the sensor). Current mirrorless models from these manufacturers continue that trend.
Samsung and Sony soon followed with mirrorless models based around larger APS-C sensors (about 23.5x15.6mm), the same size used in their DSLRs. Despite the larger sensors, the Samsung NX and Sony NEX mirrorless bodies are about the same size as the Micro Four Thirds cameras. Because the sensors are larger, however, the APS-C cameras require larger-diameter lenses. This makes the camera and lens package a bit larger than the Micro Four Thirds models, but nowhere near the size of even an entry-level DSLR package.
In 2011, Pentax introduced the smallest mirrorless, interchangeable-lens camera of all. The Q's diminutive form is possible because it's built around a compact-camera-size, 6.2x4.6mm sensor. The tiny sensor means the lenses also can be tiny: The 100mm telephoto lens (35mm equivalent) measures just 1.6x0.8 inches and weighs less than an ounce!
Most recently, Nikon joined the party with its Nikon 1 system, introducing the J1 and V1 mirrorless cameras, featuring a CX-format sensor which, at 13.2x8.8mm, is about midway in size between a typical "compact" camera sensor and Micro Four Thirds.
As you'd expect, the cameras with larger sensors deliver better image quality, but all the mirrorless models produce better image quality than typical compact digital cameras.