When we crush plastic or polythene bags, it makes a crackling sound whereas most other everyday materials do not. Why is this?
Many plastics make noise when crushed, and crackle again when opened up, e.g. when removing a candy from its plastic wrapper (to the frequent irritation of theatre patrons). As JMac commented, similar noises occur with many types of paper.
In general this happens with thin materials that do not easily stretch or compress, but that can bend without breaking and form creases and deformations that can store elastic energy. As a sheet is crushed it first bends and then suddenly buckles into a different configuration, making a cracking noise and often a permanent crease. As you continue to crush the sheet, this repeats many times on smaller and smaller scales, producing a stream of crackles. Once crushed, the many creases allow many possible configurations that the sheet can suddenly switch between if you try to open up (or otherwise further reshape) the sheet, producing clicks for every transformation. Materials such as soft cloth fold and deform easily without much resistance or sudden transformations, so the little noise they produce is primarily from rubbing friction.