It's time to restore the 11/45.

With most 'scopes one side of the input is grounded -- you have a coaxial cable with the shield connected to the 'scope case and true ground. In most, if not all, countries, one side of the mains is connected to ground too. So if you have something directly connected to mains (the common example on this list would be the the chopper circuit of an SMPSU) then you can't just clip the 'scope ground lead on it. If the input is a bridge rectifier (as it is in most SMPSUs and in the DEC regulator bricks that started this), then clipping the 'scope ground to the obvious point -- the -ve output of that rectifier -- will effectively put a diode across the mains. This is a good way to let lots of magic smoke out. The correct way round this is to run the item under test off an isolating transformer. Then no point on the secondary side of that transformer is necessarily grounded (that is the whole point of it being an _isolating_ transformer), so you can arbitrarily connect any single point in the circuit to ground. So you can clip your 'scope ground lead where you like. The dangerous way is to 'float the scope' -- that is to disconnect the mains earth from the 'scope (in the mains plug, for example. You can now connect the 'scope ground lead where you want, but since that point is not necessarily the same voltage as true ground, you can end up with the metal 'scope case at a high voltage wrt true ground. Very nasty!