To me the following points seem hard to argue against:
Oil is harder and harder to find every year (we already took the easy stuff, nobody finds super-giant fields anymore)
The peak production year was 2005 with 73.7 million barrels produced
The amount of oil produced each year is declining
The price of oil (and therefore energy) rises
All the alternatives that were supposed to fill the gap are failing to deliver
Even oil that's harder to get (e.g. in deep water) doesn't help much as it is generally produced at a slow rate
Available energy production rate (i.e. power) drops
Since nearly everything needs power to create/mine/produce prices rise
Food for example becomes more expensive as fertilizer prices rise
The average person is mystified as the price of everything seems to rise at once
Business and whole national economies are squeezed by rising prices
As businesses fail unemployment increases
Politicians are powerless, so promise general feel-good nonsense like "energy independence". Nobody even tries to tackle the problem.
Everything continues to get worse, and at an increasing rate
Within the near future the lights start to go out.
Sure there's a possibility that a form of nuclear fusion/thorium/cold fusion/zero point energy that is safe and cheap to build and operate might be invented tomorrow, but given that such things usually take a decade or so from inception to delivery it looks like there's no practical alternative on the horizon. Thermodynamics is a harsh mistress. Work out the energy in 73 million barrels of oil, and figure out how many wind farms are needed to offset a 5% decline. And then another decline the next year. Even uranium prices are rising as demand outstrips supply for just the current set of reactors.
The more we examing the situation the worse it seems to be. Some early wells had a enormous energy return on investment, e.g. for the energy of burning one barrel of oil we could pump 100 barrels from the ground. Now we are pumping wells that produce only about 5 barrels. This is known as EROEI (energy return on energy investment). EROEI is falling everywhere as all the low hanging fruit was plucking decades before, and only the difficult stuff is left. The net result is that it is ever harder to increase production rates.
Civilization runs on the constant supply of power. If that power declines 5% every year we are back to the middle ages before very long, and it's hard to develop a Friendly AI on an abacus.
One thing I've noticed a lot is reports about "Oil Sands", "Oil Shale", "Vast new possibilities of X barrels from biodiesel/microbes/algae/thermal depolymerization" etc. and none of these reports *ever* mention the *rate* of production that is expected (and years later they seem to have delivered nothing). The production rate is far more important than anything else; if the entire Earth was made of oil but we could only pump a million barrels a year for technical reasons then the total amount is pointless.
Please read at least the Peak Oil Wikipedia article before commenting. I'd rather not see a bunch of comments about "they don't even look for oil when there's 30 years of supply waiting in the ground".
2. The peak production year was 2005 with 73.7 million barrels produced
This is a little out of date. I have an old data file that supports your 73.7 megabarrel/day estimate for 2005, and that is the highest annual crude oil production recorded in the file — but my file only runs to 2009. When I check newer EIA data (scroll to the bottom of this table) that run through 2010, it turns out that 2010 (74.06 megabarrel/day) beats 2005 (73.80 megabarrel/day).
A similar pattern holds for the total oil supply (as opposed to crude oil supply) too: a bumpy plateau from 2005 (which had 84.60 megabarrel/day) to 2009, then a slight jump in 2010 (86.84 megabarrel/day).
3. The amount of oil produced each year is declining
I would've disagreed with this even before I surprised myself with the 2010 data! I would've said that production generally increased from the mid-1980s until it hit a plateau in 2005 and remained about constant since. I would've expected 2010's production to be much the same, but it actually seems quite a bit higher when I include all sources of oil production.
I didn't read the Wikipedia article like you asked; it seemed unnecessary for checking a few numbers
There is some brief discussion on the Wikipedia talk page asking why the article is full of projections from 2005 that haven't been updated. I've removed the contradicted EIA statement from Wikipedia since it'd be strange for someone to claim that the EIA in early 2010 had a better estimate of 2010 production than it did in 2011, and put an update tag at the top for the rest.
To me the following points seem hard to argue against: