What's the difference between the Fancy and Fast settings in Minecraft?

This is a complete list of everything noted on the Minecraft Wiki:

  • Leaves On Fancy, tree leaves are transparent. On Fast they are opaque
  • Clouds On Fancy, clouds are 3D, on Fast they are 2D.
  • Grass On Fancy, the sides of grass blocks have the same hue as the top, on Fast they do not (they have the default hue).
  • Item drops and frames render in 3D in fancy, and flat in Fast.

Ones I know of:

  • Leaves are solid and opaque on Fast; non-solid on Fancy
  • Rain will not hit the ground on Fast; it will hit and make noise on Fancy
  • Clouds are flat on Fast; 3D on Fancy.