Keep in mind that the airlines practice something called "yield management" whereby they try to maximize the revenue on each flight, based on predicted demand.
That means that for routes that are primarily flown by business travelers, it's often easy to get heavily discounted tickets on Saturdays, when demand from business travelers is limited. But for leisure routes, the demand for seats tends to be high on weekends when many people begin and end their vacations.
As clkelley noted, Tuesday and Wednesday are good days for cheap fares. Some airlines have fares that are only available on certain days, such as Tuesday and Wednesday.
Most flights have inventory at various different fares. When one fare category sells out, there are only seats at available in a higher fare category.