Oil and gas exist in underground traps under great pressure.  When the sandstone or limestone containing the oil or gas is penetrated by the drill bit, , the oil and gas can blast out of the well with great force.
In the early days of oil drilling, there was no good way to drill holes, and at the same time, keep this great force under control.  In the picture above, a well is shown "blowing wild".  This means that the tremendous gas pressure in the reservoir thousands of feet below the ground is forcing huge amounts of oil up the hole, blowing it into the air.

The circled well in the black-and-white picture is the Mary Sudik #1, drilled by the Indian Territory Illuminating Oil Company (ITIO) in Oklahoma.  On March 26, 1930, this well blew out at 6,470 feet.  The force blew 20 pieces of heavy 30-foot drill pipe out of the hole!

The  "Wild Mary Sudik" was finally plugged off 11 days after blowing out, through the heroic efforts of dozens of people.  Six years later, the Sudik lease had produced five million barrels of oil !

During the 1991 Gulf War, the retreating Iraqi soldiers dynamited the wellheads off more than six hundred Kuwati oil wells, creating one of the biggest man-made  environmental disasters in history (left).  Since most Kuwati wells flow without pumps under their own great pressure,  the oil and gas erupted from the ground with tremendous force.  It was first estimated that it would take 2 years to repair all the wells, however the heroic and extremely dangerous job was actually done in about six months.

"Blowouts" (except for the ones deliberately started in the Gulf War) have been extremely rare for over 60 years.   Equipment was invented later that allowed the drilling crew to keep the well under total control at all times.  In addition to being one of the most dangerous situations humans can face on on earth,  a blowout is considered bad for the environment and bad for business.  Great effort is made to avoid spilling a single drop of oil on the ground, or in the water.  

Here is a modern wellhead capping a well on a clean, well-maintained, and earth-friendly oil property:

Below left is a modern, portable drilling rig used for drilling on land.  

Of course, many wells these days are drilled in the ocean.  For this job, an offshore rig, shown above, is used.