The news has been filled with reports of exoplanets, planets orbiting other stars than our sun. These have been discovered by observing the dimming of the star due to transit -- the passing of the planet between the star and us.
That led me to consider whether an observer on a planet of another star could discover the existence of Earth by observing our transit. Only if the observer has very good instruments and is orbiting one of very-few stars. Consider:
The sun has a diameter of 864,000 miles; the Earth has a diameter of 7,900 miles; the average distance between the two -- the semi-major axis of Earth's orbit -- is 92,900,000 miles. (Miles? this is from the 1958 edition of Van Nordstrom's Scientific Encyclopedia.) So the Earth will pass between any part of the photosphere and a star only if the star is within 0.53 degree of the ecliptic plane. It will intercept 0.00914 of the sun's radiation.
Mercury will transit for any observer circling a star within 1.38 degrees of it's orbital plane, but it has less than a tenth of the area, and thus will intercept less than a tenth of the light that Earth does. Jupiter will intercept 0.083 of the sun's light -- a significant occlusion -- but only for observers within a tenth of a degree of its orbital plane.
Now, of course, most of the planets discovered have been much closer to their primaries than Earth is to the Sun. Also, the planetary orbits in the Solar System are through planes somewhat near to the rotational plain of the galaxy.
Even so, there must be many more close stars with orbiting planets which we cannot observe simply because the line of observation is too far outside the plane of planetary orbit.