Cervelo started out with very large downtubes in an airfoil shape for strength and aerodynamics. They've since scaled it back as the Kamm style foil (truncated airfoil) has become popular. Cervelo bikes have very skinny seatstays; the company says they aren't required for frame strength, just to satisfy UCI requirements.
Klein had some radical bikes with only a downtube and it was huge.
The monostay is supposedly stronger than the "fastback" or "side tack" stays but I like the look of the fastback stays myself.
Cinelli came up with this style, also seen on 3Rensho
And there's the wrapped seatstay