Summary: We instinctively imagine that 'they' will invent something to replace cheap oil. Or other power sources will be expanded to take over the role. What about hydroelectric power? Isn't it cheap, non-polluting, and can't it be used to split the water molecule into oxygen and hydrogen gas, with the hydrogen gas being used in fuel cells for vehicles?

Natural gas doesn't cut it. Here is a table, using data from BP Amoco's 'Statistical review of world energy 2000'.
I have rounded the figures up or down to the nearest whole number.
 

Some countries, such as Japan and France, are significant gas consumers and yet  don't have their own gas reserves. Yet their consumption would have to be doubled or trebled to replace even half their existing oil use. This increase can only come from imports of other countries reserves. When that happens, the life of the 'donor' countries reserves goes down.

When the oil price goes to $US48 a barrel and stays there, as it obviously will, it will become economic to make synthetic petroleum from natural gas. But, first, it will be hugely expensive by definition, and second, competition for the gas reserves will have pushed the price of gas up to the point where the economics of making the huge capital investments aren't there until a much higher oil cost than $US48 per barrel.
 
In addition, natural gas has to be made liquid for transport. LNG, natural gas in its liquid form, is primarily methane (other hydrocarbons and gases such as nitrogen boil off in liquification), which must be cooled to minus 259 degrees Fahrenheit (-161 degrees Celsius) to become liquid. Special ships are needed - basically huge floating thermos flasks - to keep the gas liquid in transport.

At 2003 there were about 136 such ships, transporting 120 million metric tonnes of gas a year. If the USA, for example, powered half the vehicles on US roads with gas (and used gas for no other purpose, including power generation), it would deplete its own reserves within 4 years. After that, even if all the existing LNG transporters in the world travelled only to USA, they still couldn't shift gas fast enough to supply gas to all who wanted it for their auto.

Even West Eurasia (Europe), physically much closer to major to major gas fields, would need new gas supplies to be transported long distances in significantly large capacity pipelines; such pipelines which don't yet exist. In theory, gas could be piped to West Eurasia overland from Russia, Turkmenistan, Iran, and the Middle East; perhaps even Algeria in North Africa.

In fact, there is competition for where a pipeline should go. There is competition from East Eurasia (China) and from Asia (India) for the gas and for placing the pipelines advantageously to their needs. The route of the pipeline must be through some of the most unstable (partly due to big country power plays), corrupt, and impoverished countries in the Eurasian continent.

West Eurasia does have the huge advantage of being able to import liquid natural gas by sea the short distance from the Middle East fields to West Eurasia via the Suez canal. Nigerian gas is also close at hand by sea. The limiting factor will be, once again, insufficient LNG tankers, and limited gas terminals.

Any action you take after reading the material here is soley your responsibility - seek advice from others, read critically and widely, don't accept everything you read here. You have been warned! Question everything.