If the circuit you're probing has a ground that is referenced to mains earth, then you can attach the scope ground clip to that point and probe away.
If the ground is not mains earth referenced, attaching the scope ground clip could cause problems, because you've now mains referenced that point and the circuit. If you connect a second scope ground clip to anywhere other than the same point, you've now shorted the two ground clips and everything in their path. You should generally be fine probing a floating circuit.
It is not a good idea to float any device that is grounded. It is grounded for a reason. If you float your scope and the chassis gets charged with a voltage, you're screwed. Same goes for the thing you're probing. Once again, if you float your circuit, and you connect a scope ground clip, then you've grounded the circuit again, this time through the probe instead of the wire leading out the back of the chassis. So careful if using multiple ground clips.
If you're unsure if a point is a ground or a mains earth referenced ground, then use a meter to find out.
As Tautech mentioned, if you need to, remove the ground clips from the probes and use the scope as you would a multimeter by using the difference operation in the math menu of the scope.
Otherwise, get a discrete differential probe.