In 1989, Voyager 2 did a fly-by of the planet Neptune. The orignal plan for the Grand Tour would have included Pluto, but the Voyager series was reduced from four craft to just two.
The New Horizons craft, launched in 2006, is expectedmade it's closes approach to arrive in the Pluto-Charon system in on July of14, 2015, at 11:49 UTC (2,500 km/7,800 mi). Technically, Neptune willis still be the most distant visited "planet" since Pluto has been reclassified as a dwarf planet.
More generally, regarding the furthest explored astronomical "feature", in 2013, it was determined that Voyager 1 crossed the heliopause and entered interstellar space. The nature of the heliopause is more subtle, though, and probably not directly observable without instrumentation.