Around the world, there are many different types of electric plugs, which makes things hard on the traveler. That gizmo you bought in Hong Kong? Not gonna work in Romania. That shaver you bought in France is useless in Utah. And if you plug an American computer into a Chinese power socket with an adapter, "BOOM!" you have no computer anymore! (Just a fancy smoking paperweight!)
Why? For one, there are four different electrical standards that would cause problems if cross-connected. But also, different countries developed their electrical grids independently of each other, often to fulfill local requirements at the time of construction. England's plugs, for instance, have fuses built into the plug, to account for there being a gross shortage of fuses at the time. They figured that they could put off installing fuses until there were more appliances that needed them. This has so far worked out rather well. It makes power cords more expensive and complicated, true, but it also means that electrical appliances at worst knock themselves off the grid, whereas my circuit breaker would darken the entire section of the house.
Some attempts have been made to combine zones. The UK's 240V and mainland Europe's 220V have been moving towards a combined 230V combined grid, slowly, but surely.
While it would be bad to connect an appliance expecting 110V to a socket that provides 220V, many plug compatibilities persist out of force of habit. A country has a set of plugs because that's the way it's always been for them, and things from out of the country are rare enough that a traveler will just get an adapter.
In the United States, the only country that I have seen extensively, we use what wikipedia describes as "Plug type B," which vaugely resembles the emoticon ":o", and provides 110V at 60 Hz. We also have NEMA 10 connectors providing 220V at 60Hz for washing machines and driers. (And hypothetically other things, but I've never seen this used for anything other than washing machines and driers.)
I think the most interesting idea for a worldwide system is based on the USB standard for computers, which can provide 5V for powering devices. The system would have a USB-style rectangular plug, and when first plugged in, would provide 5V. The device could use the electrical connection to ask for a certain voltage, and the socket could change its voltage to match. This would be immensely more complex than any existing system, but it would be universal, and once implemented, could accommodate essentially any electrical demand, in the same house. On the downside, USB plugs come in all kinds of styles, and all appliances would need voltage-negotiation circuitry so as to get anything other than 5V. (5V selected because it's low enough not to fry even delicate computer parts.)
Alternatively, we could declare one existing standard to be the standard. This would likely be the "Type C" Europlugs at 220V, which is implemented in the most number of countries.