Asteroids
Most asteroids orbit in the asteroid belt between Mars and Jupiter. For this reason, transits of the Sun by asteroids are rare from Earth's perspective, but would not be uncommon from the perspective of Jupiter. Still, high inclination of many asteroid orbits would make this less common that it would be otherwise. One example of a forthcoming asteroid transit visible from Jupiter will be that of 4 Vesta, which will transits the Sun on January 4, 2044, with an angular diameter of 0.24".
From the perspective of Earth, the only types of asteroids that can transit the Sun are those with orbits that take them between the two bodies. These include Aten asteroids (including Apohele asteroids and the hypothetical Vulcanoid asteroids) and some Apollo asteroids (perhaps including quasi-satellites of Earth). Unfortunately, observations of such transits are difficult because all of these asteroids are only a few kilometres in diameter at most, so that their angular diameter is too tiny to observe against the Sun.
One example was the May 16, 1990 transit of 3838 Epona with a diameter of 2.5 km. At a distance of 0.53 AU from Earth, its angular diameter was only 7 milliseconds of arc, far too small to see. Similarly, asteroid 30825 (1990 TG1) transited on April 14, 2005 but was again unobservable, having an angular diameter of about 0.05", and 2101 Adonis transited on September 24, 2007 with an even smaller angular diameter of only 0.005".
In theory, if a transit took place during a very close approach by a near-Earth asteroid, it might be observable. However, no such asteroid transits have been observed up to the present time.
Read more about this topic: Transit Of Minor Planets