Cables are magnetically attracted to magnets in straps and other items such as electronic devices. The cables may contain signal lines to convey power and/or data. Magnetic material that is attracted to magnetic fields may be incorporated into the signal lines and/or other structures in the cables. The straps may have flexible magnets and/or other magnets extending along their lengths. The magnets of the straps create magnetic fields that attract the cables. Electronic devices may also have housings that contain magnets to attract the cables. Using magnetic attraction, cables can be removably attached to straps and other items during operation of an electronic device, thereby helping to prevent tangling of the cables.