There's no such thing as a globally applicable "good" SNR. To make a earthbound comparison:
While your good old analog TV needs maybe an SNR of 40 dB to be somewhat enjoyable, GPS reception on very similar frequencies can work with signal well below the noise floor, so let's say -5 dB.
What SNR you'll need depends on how fast you want to transport data. And as there's very different mission needs for communication, there's very different needs for SNR.
Voyager sends low-rate. If I read this very related question correctly, Voyager's signals have a power of -152.6 dBm (that's 10⁻¹⁵ milliwatt) at earth.
Depending on the communications mode, different bandwidths are used, but documentation suggests a 12 dBHz bandwidth, leading at earth room temperature to a noise receiver power of -174 dBm/Hz + 12 dBHz + NF. We can build good amplifiers these days, so NF=0 dB is a reasonable approximation.
We end up at -162 dBm noise, and -153 dBm signal – a solid SNR of 9 dB.
For the BPSK modulation used, together with the high degree of channel coding applied, that's plenty.
You could, assuming sufficient synchronization and stability, work with way, way less – rule of thumb says BPSK works down to ca 4 dB, I think.