The transit was a  
          very rare astronomical event
 that would not be seen again for another 105 years.
Observers in north and central America, and the northern-most parts of South America saw the event start just before local sunset.
The far northwest of America, the Arctic, the western Pacific, and east Asia witnessed the entire passage.
While the UK and the rest of Europe, the Middle East, and eastern Africa waited for local sunrise to try to see the closing stages of the transit.
Venus appeared as a small black dot moving slowly but surely across the solar disc.  The traverse lasted more than six and a half hours.
Some of the best pictures of the event were provided by the  
          US space agency's (Nasa) Solar Dynamics Observatory
, which studies the Sun from a position 36,000km above the Earth.
"We get to see Venus in exquisite detail because of SDO's spatial resolution," said agency astrophysicist Dr Lika Guhathakurta.
"SDO is a very special observatory. It takes images that are about 10 times better than a high-definition TV and those images are acquired at a temporal cadence of one every 10 seconds.  This is something we've never had before."
Many citizens keen to observe the transit first hand attended special events at universities and observatories where equipment for safe viewing had been set up.
In Hawaii, one of the best places to see the whole event, the university's  
          Institute of Astronomy
 set up telescope stations on Waikiki beach.
"We've had 10 telescopes and the queues have been 10 deep to each telescope all day long," said the institute's Dr Roy Gal.
"It's a great opportunity to get people excited and teach them stuff. I was hoping for a big turn-out, and it's been fantastic," he told BBC News.
Joe Cali
 viewed the transit on the edge of the Outback in New South Wales, Australia, another ideal vantage point.
"It is exciting. It may look like just a black dot on the Sun but if you think about it, it's one of the few times you get to see a planet in motion," he said.
UK skywatchers had to deal with quite extensive cloud conditions across the country.
"We've had total cloud and rain," said Brian Sheen from the  
          Roseland Observatory in Cornwall
.
"But we've been improving our chances by connecting with the Shetland Islands and the people up there have done rather better than we have.  We've been seeing the transit through [a feed] of one of their telescopes," he explained.
Scientists observed the transit
 to test ideas that will help them probe Earth-like planets elsewhere in the galaxy, and to learn more about Venus itself and its complex atmosphere.
Venus transits occur four times in approximately 243 years; more precisely, they appear in pairs of events separated by about eight years and these pairs are separated by about 105 or 121 years.
The reason for the long intervals lies in the fact that the orbits of Venus and Earth do not lie in the same plane and a transit can only occur if both planets and the Sun are situated exactly on one line.
This has happened only seven times previously in the telescopic age: in 1631, 1639, 1761, 1769, 1874, 1882 and 2004.
The next pair will not now occur until 2117 and 2125.
The phenomenon has particular historical significance. The 17th- and 18th-Century transits were used by the astronomers of the day to work out fundamental facts about the Solar System.
Employing a method of triangulation (parallax), they were able to  
          calculate the distance between the Earth and the Sun - the so-called astronomical unit (AU)
 - which we know today to be about 149.6 million km (or 93 million miles).
This allowed scientists to get their first real handle on the scale of things beyond Earth.
In pictures: Transit of Venus
Venus transit: Your pictures
Modern instrumentation now gives us very precise numbers on planetary positions and masses, as well as the distance between the Earth and the Sun. But to the early astronomers, just getting good approximate values represented a huge challenge.
This is not to say the 2012 Venus transit was regarded as just a pretty show with no interest for scientists.
Planetary transits have key significance today because they represent one of the best methods for finding worlds orbiting distant stars.
Nasa's Kepler telescope
, for example, is identifying thousands of candidates by looking for the tell-tale dips in light that accompany a planet moving in front of its host sun.
These planets are too far away to be visited by spacecraft in the foreseeable future, but scientists can learn something about them from the way the background star's light is affected as it passes through the planetary atmosphere.
And observing a transiting Venus, which has a known atmospheric composition, provides a kind of benchmark to support these far-flung investigations.
Researchers also took a close look at Venus itself during the transit, used the occasion to probe the middle layers of the planet's atmosphere - its mesosphere.
They were  
          looking for a very thin arc of light, called the aureole
, which can only be seen when Venus appears to just touch the edge of the Sun's disc at ingress and egress.
The brightness and thickness of the aureole depends on the density and temperature of the atmospheric layers above Venus's cloud tops.
Observations of the aureole were being combined with data from  
          Europe's Venus Express spacecraft
 in orbit around the planet to provide information on high-altitude winds.
The Venusian atmosphere experiences super-rotation. That is - the whole atmosphere circles the planet in four Earth days, on a body that turns around just once in 243 Earth days.
Jonathan.Amos-INTERNET@bbc.co.uk and follow me on  
          Twitter
Planet Venus has put on a show for skywatchers by moving across the face of the Sun as viewed from Earth.