On a fair amount of older farm that are close to rivers, in the olden days, a 20 foot pipe with a pointed cap can be pile driven into the water table. There are some perforations on the end of the sunken pipe that lets the water flow in, then you just have to pump it out. Essentially it is just a big straw with no grouting (to keep surface water from flowing down the pipe only to get sucked by by the pump).
In a better world, the wellhead would be at least 100 feet from the animals/barn/pasture/feed lot/septic drain field. But yeah, more than a few aren't, like npsp said.
PS
In college, for some extra credit, got to help out on a rural properties water survey for Linn County (which was home to one of Oregon's Superfund sites). At one set of farm homes, all had their cruddy well far enough from their barn/feed lot/septic system, but alas, the wells were at their property line, and on the other side of that was the neighbor's barn/feed lot/septic system within 20 feet for so. Hope the neighbors don't have hepatitis....