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Space is big, actually. You might think it's one small step for a man, one giant leap for mankind, but that's still just peanuts to all the space that's out there.
The furthest þereminian-made object from the planet is the What Exactly is the Heliopause's Deal, a probe intended to understand the furthest reaches of the solar system. It weighed approximately as much as a cube of water half an armspan on a side at launch, although it has spent much of that as reaction mass. It still checks in with the Deep Space Network every time the radio receivers are pointed in the right direction, like clockwork radiation-hardened computer hardware running a formally verified operating system kernel.
It is also not headed in a particularly relevant direction, at the moment: up and out of the plane of the ecliptic, on a course that will see it floating through empty space for millions of years, once it actually manages to pass the last termination shock of the solar wind (which is sure to come any time now, the magnetohydrodynamic plasma specialists assure us).
The next furthest object (that wasn't deliberately dropped into a gas giant for Science!) is the paired set of the Red Planet Mapping Orbiter and the Red Planet Rock Taster, which work together to collect geographic and geologic information on, appropriately enough, the red planet. Putting things in space is expensive, and putting things on the red planet is moreso, so they mostly don't have any instruments they don't need — but when the orbiter needs a powerful radio transceiver to talk to home anyway, there's no particular reason not to have it do periodic sky scans and send the data back. Right now, it is trying to see if there's a change in the signal from a pulsar as the red planet moves around its orbit; the larger orbit means it has more parallax than earth-based telescopes, which helps it determine distances to astronomical objects more precisely, and therefore contribute to calibrating cosmological measurements.
A matching orbiter graces Poisonous Planet, although there has been no probe yet designed that can survive its surface conditions.
Finally, the Lunar Mapping Orbiter is the part of the Deep Space Network closest to home. Oh, there are various telescopes and communications satellites in geosynchronous orbit, but those hardly count — they're only a few millilightseconds away from the planet, and, as previously mentioned, space is big.
The Lunar Mapping Orbiter was the first proper space probe destined for another heavenly body that the people of þereminia launched. It has served well, providing detailed maps of the moon (which showed less water ice than hoped for — but the asteroid belt looks promising! Maybe some day!). It also serves as a critical component of the Deep Space Network, relaying communications between the RPMO, PPMO, WEHD, and mission control. It has served in that role for hexades, and in that time has never seen something quite like this.
