- Simon L., Portland
Yes, it can. First, we should explain that a transit is the direct passage of a planet across the Sun from a given perspective. Only two planets, Mercury and Venus, can transit the Sun from our perspective. Mercurian transits occur about 13-14 times per century. The last transit of Mercury occurred in November 2006. The next one happens on May 9, 2016. Transits of Venus are less frequent. They generally occur in 8-year pairs separated by more than a century. The last two Venusian transits happened on June 6, 2012 and June 8, 2004. The next transit of Venus won't happen until December 11, 2117.
A transit can only occur when an inferior planet - one that is closer to the Sun - moves directly between the Sun and a planet farther away. As the planets are all inclined at different angles relative to the solar system's plane, most of the time an inferior planet will be either north or south of the plane connecting a more distant planet and the Sun. Unless the planets are more precisely aligned, a transit will not occur.
The last transit of Earth from Mars occurred on May 11, 1984. The next transit of Earth from Mars won't happen until November 10, 2084. The above image, issued by NASA, shows us how Earth will appear from Mars during this transit. Also, and quite excitingly, the Moon will also appear to transit the Sun, as well. It will either follow or precede Earth across the Sun. If you miss the 2084 Earth transit event, you'll have to wait until November 15, 2163. Transits of Earth from Mars are presently only possible in May and November. (Curiously, transits of Mercury from Earth occur in either May or November right now. Transits of Venus happen in only June or December.)
The following two transits of Earth from Mars occur on May 10, 2189 and then again on May 13, 2268.
Transits of Earth from Jupiter are more common. The last occurred on January 5, 2014. The next won't happen until January 20, 2026. Then, another occurs on June 24, 2055, followed by another on June 29, 2067.
The next transit of Earth from Saturn occurs on July 20, 2020. Curiously, we might have the chance to observe the previous transit on January 13, 2005, because the Cassini probe was in the system. However, this transit happened around the time the craft was deploying the Huygens craft onto Titan, and completing those complex maneuvers was more important that capturing images of an Earth transit. Also, Earth's dot is very small from Saturn's distance. The next transit of Earth from Saturn after the 2020 event occurs on July 16, 2049.
Now, out of fear of losing my audience (maybe I'm too late), I'll stop here. Yes, Earth transits are possible and not that uncommon. The trick is figuring out how to observe these events considering that we're all still on or in orbit around Earth.