What is the most distant object from the earth that a spacecraft visited has visited so far? What was the mission and when did it happen?
Depending on your definition of "object," Neptune is currently the farthest. It was visited by Voyager 2 in 1989. New Horizons will be visiting Pluto in 2015
If by object you mean cosmic structure though, then Voyager 1 is currently in the Heliosheath and is expected to reach the heliopause by 2015. These are regions that describe interactions between the sun's solar wind and the interstellar medium.
We landed on Titan in 2004. That is definitely a milestone in being far away and landing on the surface of something big. Source
It's a damn shame they didn't manage to get a better photograph of the surface.