The self-cleaning property is usually connected to superhydrophobic surfaces (SHSs) where the dust particles can be easily removed by the rolling motion of droplets. It seems that superhydrophobicity (its durability is questionable nowadays) is a necessity. However here, it is disclosed that self-cleaning can also be realized on an ordinary surface by droplet impinging. The effects of surface wettability and the types of dust particles are considered. The self-cleaning is realized by two steps: (1) the pickup of particles by the water-air interface of an impinging droplet, (2) the release of the impinging droplets from the surface. It can be observed that only the trailing edges of the droplets can pick up particles when the droplets recoil from the inclined surfaces. The hydrophilic surface can also achieve self-cleaning under some conditions. This interesting finding may be helpful for the successful implementation of self-cleaning with common surfaces.