Most people get a refund on their taxes in any given year. Generally speaking around 80% of people filing taxes get a refund.
I found the historical IRS tax data going back to 1950 showing who gets refunds versus who owes taxes.
Here's a chart of the trend from 1950 to 2011 from the current IRS data set :
I am sure there are various things that drive the longer term trends. IRS tax withholding processes have undoubtedly evolved over the decades. Things like more dual income households may impact it as well. The introduction of earned income tax credits may have increased refund rates as well.
The green line indicates people who get neither a refund nor owe money. I'm assuming thats mostly for people who had no money withheld but owed nothing. Maybe people like retirees on social security and minimal other income.