USMC Harriers regularly take-off from the flight decks of US Navy ships without the aid of either a catapult or a ski-jump. However, rather than a large aircraft carrier, they are taken to sea aboard Wasp or Tarawa class amphibious assault ships, which are quite a bit bigger than the British carriers:
Harrier with no ski jump
YouTube - AV8-B Harrier Launch
The Russians use ski-jumps too for their non catapulted Su 33's - They get airborne using butch power alone.
The CVFs are pretty similar to the Russian carriers.