If you mean the actual Earth and a free-fall orbit, the orbital speed of something in low earth orbit, like the ISS, about 8 km/sec, is as fast as anything can orbit the earth.

To get really fast orbital speeds (as in, speeds that are any significant fraction of the speed of light), you need objects much, much more compact than the Earth, objects whose actual size is not that much larger than the size of a black hole with the same mass. The only non-black hole objects we know of that are anywhere close to that compact are neutron stars.