Oscilloscopes typically have multiple input channels which have a common ground (which also happens to be earth referenced). The problem is that the probes can be connected to ground through a huge alligator clip, which is very impractical and likely to cause short-circuits with other signals. For this reason, connecting each probe to ground, which is arguably the best solution, is often undesirable.
However, I find that in many cases, connecting just a single probe to GND and let the others connect to the signal only works just as well. In some cases, not connecting any probe to GND and just letting the earth reference do its job works well enough.
In which cases is it fine to leave the probes unconnected to GND ?
In the scope of this question I assume only a single device is measured (or multiple devices which already have their grounds connected)