In the TV lab we prescribed the use of an isolation transformer to galvanically separate our device under test from the mains. This made the TV safe to touch, with ONE hand. It also made the TV safe to test, i.e. to connect the ground of your oscilloscope to the circuit. But when you connect a grounded 'scope to a floating circuit, it becomes grounded again, and in principle unsafe to touch !
To get to the point, we had a law that it is forbidden to connect a power strip to an isolation transformer. Use one transformer per device. Otherwise it becomes too easy to touch two devices and find out the hard way that one is "hot" relative to the other. You cannot galvanically separate a whole building and expect the circuit to remain floating and safe.
Besides inadvertent grounding through some device there is also leakage current to ground, through capacitors. Your computer has a galvanically separated power supply, so it is safe to touch. But there is a C between the primary ground and the secondary to short-circuit the EMI of the SMPS. If the ground is not connected and you touch the case then the 50-60 Hz current through that C (and the C of the transformer) gives you a tingle. Connect 10 such devices with 10 Cs together without explicitly grounding any of them and that tingle becomes a shock. That's why you should use an outlet with ground for modern electronic devices. [edit: added schematic from another thread Henry Crun]
