Remove wp-caption but still show the image

You’ll need to use the img_caption_shortcode filter to do this. Pretty certain the alignment of the image (floating left/right) is part of the caption so you’ll lose the ability to do that with this code.

function imageOnly($deprecated, $attr, $content = null) 
{
    return do_shortcode( $content );
}
add_filter( 'img_caption_shortcode', 'imageOnly', 10, 3 );

The do_shortcode is probably overkill.

I use something very similar to change the caption output to be responsive. Tested on WordPress 3.8.1