Since version 8, the Knoppix ISO is a hybrid image that can be burnt on a DVD, but also copied to a USB stick without any change. To create a bootable Knoppix USB stick,

  1. download an ISO image of the newest Knoppix version;
  2. plug in a USB stick; WARNING: all contents of the stick will be overwritten!!
  3. determine the device path of the USB stick, by using either
    mount
    (if the USB got automounted), or
    sudo blkid -c /dev/null
  4. use dd to copy the ISO image to the USB stick:
    sudo dd if=/path/to/knoppix-image.iso of=/dev/sdX bs=16M
    (where sdX has to be replaced by the device found in point 3; WARNING: indicating a wrong device will destroy its contents without warning, so double-check the path!)

Sources