I mean it depends on the intensity of the surge, but basically you'd be making it so your PSU is unable to protect the devices from surges. The more sensitive the electronics, the more critical the ground is and CPUs are pretty darned sensitive among other things. And depending on the type of components in the PSU, "surges" also include things like inrush current. Basically, when you turn on a transformer or certain other devices, there is a surge of sometimes as much as 10 times the rated current to create the initial magnetic flux. Depending on the components, this excess energy may end up getting shunted to the ground to avoid pushing it through your electronics. So if it can't do that, you likely will blow fuses a lot when switching the power on (hopefully there are fuses), or if you're touching the case which is supposed to be grounded, you may end up getting that jolt.
Anyway, without grounded outlets, and especially if your electronics are cheaply made because many expect there to be grounding and don't build in extra components to deal with not having a ground, you are likely to significantly reduce the life of your electronics, your life, or start a fire without even considering major surges. If you have a high-end PSU, you may never have a problem until that surge happens. How stable is your power? Because even a normally small surge combined with a cheap PSU, and no ground, is pretty likely to end up in damage to electronics at the best case.