The date depends on your time zone.  Generally, for the Americas where it is visible (blue color on map below) the 2012 transit occurs the evening of Tuesday, June 5, 2012.  For Eurasia and Africa where it is visible (sage color on map), the latter part of the transit is seen the morning of June 6, 2012. The cross-hatch area in both colors experiences the 2012 Transit of Venus across six hours that span both June 5 and 6.

One of the reasons there has been confusion on the date is because of the naming convention for the titles of tables of astronomical events.  A celestial event is often listed in the title according to the date when the mid-event occurs in Universal Time.  For example, in its 6-hour time span, the middle of the transit of Venus occurs shortly after midnight on June 6, 2012, in Greenwich time.  Admittedly, the sun isn't even visible in Greenwich just after midnight, but then is the moment of "greatest transit."  Hence, accurate tables will sometimes title it as the June 6, 2012, transit of Venus.  Meanwhile, in another time zone such as Hawaii, the entire transit of Venus is visible on June 5, 2012. 

Yes, it can be tricky.  The map below by Steven van Roode shows the transit dates visually.  For additional clarity at your site, get specific times at http://www.transitofvenus.nl/details.html.