Please. We have been claiming to reach peak oil for many, MANY years now. The only difference now is that the sources we have been depending on for a long time have...
Actually, I can't think of an oil well that is drying up now...
Actually, there have been several "oil peaks"
There was the Texas oil peak and the United States oil peak. These are what you're thinking of. Texas and the rest of the US have been producing less and less oil ever since the 70's and 80's. What we are approaching- and may have already passed- is the WORLD production peak. Particularly, Saudi and Mexican oil fields. There are some places that may have as much as a decade of growth left in them, but they won't keep up with the declining global production.
There won't be riots. There won't be wars. There won't be starvation.
...Immediately.
Oil Prices will tend to increase (though not continuously- there are variations in this and short term drops are guaranteed), and alternatives, most likely a combination of small fuel sources, will arise. These will most likely not be as much as oil produces, but they will be close.
The real effects will be subtle but universal. A few things you might expect:
-Air Travel will be rarer: You can't make an electric airplane with current technology; and though fuels will be available that can run jets and aircraft, they will be more expensive, so only the wealthy will fly (until new technology is developed)
-International Trade will slow: those big boats need a lot of fuel. There will be alternatives, but these will take some time to adapt to and be expensive. Thus, more "made in the USA" stickers.
-Food will be local-grown: With fewer(not absent) Trucking and shipping, you'll see less food coming from CA in NY. And less SoCa food in NoCa. The funny thing is that organic foods will increase in price less than, well, inorganic food; you may get healthier.
-More jobs: On the farm. Whee. Beats McDonald's, though. The differece is that these farms will be smaller and closer to home.
-You will have a generator and a well: It's going to get less profitable to run the Electric company and the Water company. They will decrease service and many people at the edge of the grid will drop off entirely. Rolling black-outs may occur until new power sources are used.
It's not the end of the word, it's just annother change, and not too bad at that.