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Wikipedia states that Voyager 1 is currently farthest from Earth; it gives the distance as of Dec 3 2013 as 126.95 AU ($1.899 \cdot 10^{10}\text{ km}$) from Earth. At that distance, the speed of light delay is approximately 17 hours 36 minutes. By Dec 7 2013 it was listed as at a distance of 127.03 AU from Earth, which means it is moving away from Earth at a speed of 0.02 AU per day, corresponding to a speed (relative to Earth) of roughly 35 km/s. The speed relative to the sun is stated as approximately 17 km/s. The probe was launched, along with its sister Voyager 2, in August 1977; Wikipedia states that Voyager 2's current speed relative to the sun is slightly above 15.4 km/s at a distance from Earth of 103.00 AU as of Dec 7 2013. Since you're asking about the farthest, I focus on Voyager 1.

Exactly what might count as "amazing discoveries" is of course a matter of personal opinion rather than a strict scientific assessment, but Voyager 1 does seem to have contributed to our understanding of the outer limits of the heliosphere. As TildalWave pointed out in a comment (since deleted), it has also provided evidence of many other things, including that it has:

• Provided evidence of active volcanoes on celestial bodies other than Earth
• Sent us close-up pictures of Saturn's ring system, including detail pictures of Saturn's F ring
• Proven to still be working (although much of the on-board equipment has either been deactivated or malfunctioned) 36 years after launch, and possible to communicate with across such vast distances, and sending useful scientific data having exited the solar system; it is expected to remain operational until some time around 2025, for a nearly 50 years long active service life, whereas Voyager 2 is expected to remain operational until around 2020 for 40-45 years of service
• Sent us the "Pale Blue Dot" picture, showing Earth from 6.4 billion km (42.8 AU) away

The feat of communicating with the spacecraft (also here) might actually be quite significant in and of itself; Voyager 1 communicates with Earth (through the Deep Space Network) on frequencies near 2.3 GHz and 8.4 GHz. Unless I'm getting the calculations wrong (although the numbers do appear to be within the ballpark), free space propagation losses alone is in the neighborhood of 300 dB on 2.3 GHz and 320 dB on 8.4 GHz. Communications with Voyager is done with about 20 kW uplink into the DSN's large antennas.

Wikipedia states that Voyager 1 is currently farthest from Earth; it gives the distance as of Dec 3 2013 as 126.95 AU ($1.899 \cdot 10^{10}\text{ km}$) from Earth. At that distance, the speed of light delay is approximately 17 hours 36 minutes. By Dec 7 2013 it was listed as at a distance of 127.03 AU from Earth, which means it is moving away from Earth at a speed of 0.02 AU per day, corresponding to a speed (relative to Earth) of roughly 35 km/s. The speed relative to the sun is stated as approximately 17 km/s. The probe was launched, along with its sister Voyager 2, in August 1977; Wikipedia states that Voyager 2's current speed relative to the sun is slightly above 15.4 km/s at a distance from Earth of 103.00 AU as of Dec 7 2013. Since you're asking about the farthest, I focus on Voyager 1.

Exactly what might count as "amazing discoveries" is of course a matter of personal opinion rather than a strict scientific assessment, but Voyager 1 does seem to have contributed to our understanding of the outer limits of the heliosphere. As TildalWave pointed out in a comment (since deleted), it has also provided evidence of many other things, including that it has:

• Provided evidence of active volcanoes on celestial bodies other than Earth
• Sent us close-up pictures of Saturn's ring system, including detail pictures of Saturn's F ring
• Proven to still be working (although much of the on-board equipment has either been deactivated or malfunctioned) 36 years after launch, and possible to communicate with across such vast distances, and sending useful scientific data having exited the solar system; it is expected to remain operational until some time around 2025, for a nearly 50 years long active service life, whereas Voyager 2 is expected to remain operational until around 2020 for 40-45 years of service
• Sent us the "Pale Blue Dot" picture, showing Earth from 6.4 billion km (42.8 AU) away

The feat of communicating with the spacecraft (also here) might actually be quite significant in and of itself; Voyager 1 communicates with Earth (through the Deep Space Network) on frequencies near 2.3 GHz and 8.4 GHz. Unless I'm getting the calculations wrong (although the numbers do appear to be within the ballpark), free space propagation losses alone is in the neighborhood of 300 dB on 2.3 GHz and 320 dB on 8.4 GHz. Communications with Voyager is done with about 20 kW uplink into the DSN's large antennas.

Wikipedia states that Voyager 1 is currently farthest from Earth; it gives the distance as of Dec 3 2013 as 126.95 AU ($1.899 \cdot 10^{10}\text{ km}$) from Earth. At that distance, the speed of light delay is approximately 17 hours 36 minutes. By Dec 7 2013 it was listed as at a distance of 127.03 AU from Earth, which means it is moving away from Earth at a speed of 0.02 AU per day, corresponding to a speed (relative to Earth) of roughly 35 km/s. The speed relative to the sun is stated as approximately 17 km/s. The probe was launched, along with its sister Voyager 2, in August 1977; Wikipedia states that Voyager 2's current speed relative to the sun is slightly above 15.4 km/s at a distance from Earth of 103.00 AU as of Dec 7 2013. Since you're asking about the farthest, I focus on Voyager 1.

Exactly what might count as "amazing discoveries" is of course a matter of personal opinion rather than a strict scientific assessment, but Voyager 1 does seem to have contributed to our understanding of the outer limits of the heliosphere. As TildalWave pointed out in a comment (since deleted), it has also provided evidence of many other things, including that it has:

• Provided evidence of active volcanoes on celestial bodies other than Earth
• Sent us close-up pictures of Saturn's ring system, including detail pictures of Saturn's F ring
• Proven to still be working (although much of the on-board equipment has either been deactivated or malfunctioned) 36 years after launch, and possible to communicate with across such vast distances, and sending useful scientific data having exited the solar system; it is expected to remain operational until some time around 2025, for a nearly 50 years long active service life, whereas Voyager 2 is expected to remain operational until around 2020 for 40-45 years of service
• Sent us the "Pale Blue Dot" picture, showing Earth from 6.4 billion km (42.8 AU) away

The feat of communicating with the spacecraft (also here) might actually be quite significant in and of itself; Voyager 1 communicates with Earth (through the Deep Space Network) on frequencies near 2.3 GHz and 8.4 GHz. Unless I'm getting the calculations wrong (although the numbers do appear to be within the ballpark), free space propagation losses alone is in the neighborhood of 300 dB on 2.3 GHz and 320 dB on 8.4 GHz. Communications with Voyager is done with about 20 kW uplink into the DSN's large antennas.

Wikipedia states that Voyager 1 is currently farthest from Earth; it gives the distance as of Dec 3 2013 as 126.95 AU ($1.899 \cdot 10^{10}\text{ km}$) from Earth. At that distance, the speed of light delay is approximately 17 hours 36 minutes. By Dec 7 2013 it was listed as at a distance of 127.03 AU from Earth, which means it is moving away from Earth at a speed of 0.02 AU per day, corresponding to a speed (relative to Earth) of roughly 35 km/s. The speed relative to the sun is stated as approximately 17 km/s. The probe was launched, along with its sister Voyager 2, in August 1977; Wikipedia states that Voyager 2's current speed relative to the sun is slightly above 15.4 km/s at a distance from Earth of 103.00 AU as of Dec 7 2013. Since you're asking about the farthest, I focus on Voyager 1.

Exactly what might count as "amazing discoveries" is of course a matter of personal opinion rather than a strict scientific assessment, but Voyager 1 does seem to have contributed to our understanding of the outer limits of the heliosphere. As TildalWave pointed out in a comment (since deleted), it has also provided evidence of many other things, including that it has:

• Provided evidence of active volcanoes on celestial bodies other than Earth
• Sent us close-up pictures of Saturn's ring system, including detail pictures of Saturn's F ring
• Proven to still be working (although much of the on-board equipment has either been deactivated or malfunctioned) 36 years after launch, and possible to communicate with across such vast distances, and sending useful scientific data having exited the solar system; it is expected to remain operational until some time around 2025, for a nearly 50 years long active service life, whereas Voyager 2 is expected to remain operational until around 2020 for 40-45 years of service
• Sent us the "Pale Blue Dot" picture, showing Earth from 6.4 billion km (42.8 AU) away

The feat of communicating with the spacecraft (also here) might actually be quite significant in and of itself; Voyager 1 communicates with Earth (through the Deep Space Network) on frequencies near 2.3 GHz and 8.4 GHz. Unless I'm getting the calculations wrong (although the numbers do appear to be within the ballpark), free space propagation losses alone is in the neighborhood of 300 dB on 2.3 GHz and 320 dB on 8.4 GHz. Communications with Voyager is done with about 20 kW uplink into the DSN's large antennas.

Wikipedia states that Voyager 1 is currently farthest from Earth; it gives the distance as of Dec 3 2013 as 126.95 AU ($1.899 \cdot 10^{10}\text{ km}$) from Earth. At that distance, the speed of light delay is approximately 17 hours 36 minutes. By Dec 7 2013 it was listed as at a distance of 127.03 AU from Earth, which means it is moving away from Earth at a speed of 0.02 AU per day, corresponding to a speed (relative to Earth) of roughly 35 km/s. The speed relative to the sun is stated as approximately 17 km/s. The probe was launched, along with its sister Voyager 2, in August 1977; Wikipedia states that Voyager 2's current speed relative to the sun is slightly above 15.4 km/s at a distance from Earth of 103.00 AU as of Dec 7 2013. Since you're asking about the farthest, I focus on Voyager 1.

Exactly what might count as "amazing discoveries" is of course a matter of personal opinion rather than a strict scientific assessment, but Voyager 1 does seem to have contributed to our understanding of the outer limits of the heliosphere. As TildalWave pointed out in a comment (since deleted), it has also provided evidence of many other things, including that it has:

• Provided evidence of active volcanoes on celestial bodies other than Earth
• Sent us close-up pictures of Saturn's ring system, including detail pictures of Saturn's F ring
• Proven to still be working (although much of the on-board equipment has either been deactivated or malfunctioned) 36 years after launch, and possible to communicate with across such vast distances, and sending useful scientific data having exited the solar system; it is expected to remain operational until some time around 2025, for a nearly 50 years long active service life, whereas Voyager 2 is expected to remain operational until around 2020 for 40-45 years of service
• Sent us the "Pale Blue Dot" picture, showing Earth from 6.4 billion km (42.8 AU) away

The feat of communicating with the spacecraft (also here) might actually be quite significant in and of itself; Voyager 1 communicates with Earth (through the Deep Space Network) on frequencies near 2.3 GHz and 8.4 GHz. Unless I'm getting the calculations wrong (although the numbers do appear to be within the ballpark), free space propagation losses alone is in the neighborhood of 300 dB on 2.3 GHz and 320 dB on 8.4 GHz. Communications with Voyager is done with about 20 kW uplink into the DSN's large antennas.

Wikipedia states that Voyager 1 is currently farthest from Earth; it gives the distance as of Dec 3 2013 as 126.95 AU ($1.899 \cdot 10^{10}\text{ km}$) from Earth. At that distance, the speed of light delay is approximately 17 hours 36 minutes. By Dec 7 2013 it was listed as at a distance of 127.03 AU from Earth, which means it is moving away from Earth at a speed of 0.02 AU per day, corresponding to a speed (relative to Earth) of roughly 35 km/s. The speed relative to the sun is stated as approximately 17 km/s. The probe was launched, along with its sister Voyager 2, in August 1977; Wikipedia states that Voyager 2's current speed relative to the sun is slightly above 15.4 km/s at a distance from Earth of 103.00 AU as of Dec 7 2013. Since you're asking about the farthest, I focus on Voyager 1.

Exactly what might count as "amazing discoveries" is of course a matter of personal opinion rather than a strict scientific assessment, but Voyager 1 does seem to have contributed to our understanding of the outer limits of the heliosphere. As TildalWave pointed out in a comment (since deleted), it has also provided evidence of many other things, including that it has:

• Provided evidence of active volcanoes on celestial bodies other than Earth
• Sent us close-up pictures of Saturn's ring system, including detail pictures of Saturn's F ring
• Proven to still be working (although much of the on-board equipment has either been deactivated or malfunctioned) 36 years after launch, and possible to communicate with across such vast distances, and sending useful scientific data having exited the solar system; it is expected to remain operational until some time around 2025, for a nearly 50 years long active service life, whereas Voyager 2 is expected to remain operational until around 2020 for 40-45 years of service
• Sent us the "Pale Blue Dot" picture, showing Earth from 6.4 billion km (42.8 AU) away

The feat of communicating with the spacecraft (also here) might actually be quite significant in and of itself; Voyager 1 communicates with Earth (through the Deep Space Network) on frequencies near 2.3 GHz and 8.4 GHz. Unless I'm getting the calculations wrong (although the numbers do appear to be within the ballpark), free space propagation losses alone is in the neighborhood of 300 dB on 2.3 GHz and 320 dB on 8.4 GHz. Communications with Voyager is done with about 20 kW uplink into the DSN's large antennas.