The debate about peak oil can be summed up in two graphs. So, excuse me for a moment as I revert to my larval form as an economics professor before I blossomed into the beautiful butterfly I've become.
Here's the first pretty graph:
This graph represents a the short run market for oil. The supply curve is fairly flat over some range, and then turns sharply upwards. This reflects the fact that in the short term at least there is a fixed maximum capcity that can be pumped out. The arrows reflect how the short run market is evolving over time. The demand curve is shifting outwards as worldwide demand grows, and the supply curve is shifting inwards at some speed as oil deposits are used upand the deposits which are the cheapest to extract are used up first. Market price is obtained at the point of intersection of the curves.
What we learn from this graph is that if the demand curve intersects the supply curve is at or near capacity, then price spikes can be large and sudden. This can be exacerbated by speculators boosting demand and potentially California-style gaming of the system through deliberate slowdowns in delivery/refinery (obviously refinery is about the market for oil-derived products, not oil, but the story is the same). If ever we're in a situation like this in the short term, even if there's a whole mess of easily extracted deposits sitting out there, we've got problems. Massive oil price spikes and supply disruptions would result, even if we haven't actually "run out of oil."
Long run, then fundamental question is - how fast are the demand and supply curves moving, and what is the shape of the long run supply curve. If we think now of the "market for oil and close substitutes," allowing for the possibility of some sort of grand technological transformation or the discovery of massive dilithium mines, the question is whether the long run supply curve is very steeply sloped, reflecting few new oil deposits or no new technology, or if it is more gently sloped, looking more like this:
Either way, serious energy market problems are more than possible even if there's still plenty of hot tasty oil just waiting for the taking if that demand curve is flirting with the production capacity level. It's hard to comprehend the impact on the world economy if even a temporary massive oil price spike combined with some supply disruptions occurs. It's also hard to imagine that such an event won't occur at some point. Long run, however, the future depends on how much oil is out there, how fast worlwide demand is increasing, and how fast new substitutes for oil come into being, either by using existing technologies (wind,nuclear, etc...) or finding new ones.
If we have oil supply problems, the worst hit areas will be those which at the time of the supply problem there aren't any close substitutes. Electricity can be produced a variety of ways, but right now cars need oil. I'll leave it to the experts as to whether hydrogen will be a better energy storage device for cars than batteries storing electricity, but weaning automobiles away from oil dependency would go a long way to cushioning us against a potential price shock.