Venus transit used to be very important for determining Earth-Sun distance (so called Astronomical Unit (AU)), which...
Venus transit used to be very important for determining Earth-Sun distance (so called Astronomical Unit (AU)), which is a base for many astronomical and cosmological measurements. 

Before Kepler, Aristarchus/Hipparchus/Ptolemy used Earth/Moon/Sun naked-eye measurements, and AU value was off by a factor of 3-5x.

Godefroy Wendelin repeated Aristarchus' measurements in 1635 with a telescope, but still was off by a factor of 2x.

Johannes Kepler published his radical first and second laws in 1609. Ever since he published his third law in 1619, relative distances Venus-Earth or Venus-Sun (in AUs) were easy to determine precisely, simply from Venus' orbital period. Absolute distances are much harder. Precisely measuring Venus' (or Mars') parallax with respect to stars was not possible at the time.

In 1629,  one year before his death in 1630, Kepler predicted Venus transit in 1931 (visible from America, but not from Europe), and near-miss in 1639, and was urging astronomers to observe them. He was right about 1931, but wrong about 1639. Actual transit was predicted by Jeremiah Horrocks (who also realized they come in pairs, 8 years apart).

Horrocks was also the first to realise that measuring Venus' parallax during transit could give much higher precision, because we can measure time (say of first contact), much more precisely then angles. Horrocks did observe it from England. together with one more nearby observer, William Crabtree. But since neither of the observations were very precise time-wise or far enough apart, exact relative times could not have been obtained, although they did yield precise angular size of Venus (to 1 arcsec), and did confirm Kepler laws.

In 1672, Cassini & Richer measured parallax of Mars at opposition with AU precision of ~10%.

Halley (of the comet fame) in 1716 predicted next transit pair at 1761 and 1769, again urging astronomers to observe it, Halley expecting parallax precision of 0.2% if the time of contact could be measures to within 2 sec. In 1761, 8 European countries sent 120 observers to 50 expeditions to far corners of the Earth, but when they all came back, precision was only 25%, due, in part, to the weird unexpected "black drop effect". Neither Horrocks nor Crabtree saw the first or last contact, so nobody knew about it, and weren't prepared, and 25% was quite worthless. This is also when also when Lomonosov observed a ring of light surrounding Venus as it transited the Sun and concluded that Venus has an atmosphere. Foreign pooh-poohers (злопыхатели) claim that he noticed, because he was the only one idly watching, instead of busily making measurements, like everyone else. Clearly sour grapes [1].

In 1769, they were at it again, with 150 astronomers from 11 nations, one expedition led by Capt. James Cook, whom aborigines allegedly ate later, but not really. This time, the precision achieved was 2.2%.

Next pair of transits was 1874 and 1882. By then photography was invented, and precision was 1.6%.

In 1961, Richard Goldstein, a graduate student at Caltech, did radar ranging of Venus from the Goldstone Tracking Station, with precision of 0.1% (150,000 km)

In 1976 telemetry from Venus probes, made precision 0.0001% (150 km), and by 2009 - 0.000,000,3% (0.5 km).
 
Next pair of transits were 2004 and 2012. By then, it was used mainly to practice study of exosolar planets and to entertain kids. Reenactment of AU measurements by Venus parallax, achieved precision of 0.007% (12,000 km).

[1] You can rediscover it here:  https://plus.google.com/112065430692128821190/posts/56yxuDYqEfn

http://en.wikipedia.org/wiki/Transit_of_Venus
http://en.wikipedia.org/wiki/Astronomical_unit
http://books.google.com/books?id=OApp_VtQnkIC
http://en.wikipedia.org/wiki/Transit_of_Venus

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