What is the most distant planet from the earth that a spacecraft visited has visited so far? What was the mission and when did it happen?
The New Horizons craft, launched in 2006, made it's closes approach to Pluto on July 14, 2015, at 11:49 UTC (2,500 km/7,800 mi). Technically, Neptune is 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.
Among objects called "planets" and defining a visit as actually making contact with the body, I nominate Jupiter as second farthest, and Saturn as No. 1. Galileo included a space probe that descended from orbit, entered what we now call Jupiter proper, and performed and reported analysis. It did not last long, but it counts as a visit in my book. Similarly for Saturn, where Cassini made its atmospheric entry even if (as was the case for Galileo diving into Jupiter) it was the craft's swan song.