Make views slideshow responsive - remove inline styles
The flexslider module mentioned above seems great with it's mobile swipe support, but only images are supported and I needed videos slideshow, with overlays support. So I've added the following lines in my theme's CSS file and it worked:

.views_slideshow_cycle_main { width: 100%; }
.views_slideshow_cycle_main .views-slideshow-cycle-main-frame { width: 100% !important; height: auto; }
.views_slideshow_cycle_main .views-slideshow-cycle-main-frame-row { width: 100% !important; height: auto; }
.views_slideshow_cycle_main .field-content { max-width: 100%; width: 100%; }
.views_slideshow_cycle_main .field-content img { max-width: 100%; width: 100%; height: auto; margin: 0; padding: 0; }


With SCSS, it may be easily written as: 

.views_slideshow_cycle_main {                                                      
  width: 100%;                                                                     
 .views-slideshow-cycle-main-frame {width: 100% !important; height: auto;}         
 .views-slideshow-cycle-main-frame-row {width: 100% !important; height: auto;}     
 .field-content { max-width: 100%; width: 100%;}                                   
 .field-content img { max-width: 100%; width: 100%; height: auto; margin: 0; padding:0;} 
}   


The overlays were added by views_slideshow_xtra_overlay.

Adapted from This discussion