What did Shakespeare's father do for a living?
One of the most interesting things about Shakespeare is that, unlike almost every other successful writer of his time, he was working class. His father was in trade in Stratford, and Shakespeare was very lucky in that the town council of Stratford paid for the boys (unfortunately, not the girls) to be educated in local schools. This gave him an opportunity which would not have been available to other boys of Shakespeare's class in other towns.
Shakespeare's father, Richard, was a farmer and subsequently a glover-maker in Stratford. He had a few brushes with the law, as when he was fined for creating, effectively, a hygiene hazard outside his house involving an outside privy or toilet. Because of this background, Shakespeare was derided in his own time as an "upstart crow," as he had not been to Cambridge or Oxford like other writers. It is widely believed that classism of this sort is what gave rise to the idea that Shakespeare "could not" have written all of his plays and poems; people simply didn't believe that a working class boy could be so capable, although he had been educated at grammar school.
Shakespeare's father had many jobs, as a matter of fact. Some other interesting details:
He was a farmer.
He was the official town beer-taster.
He traded wool, and it is believed that he did this trading illegally.
He was a money lender - what might today be called a "loan shark".
John Shakespeare was fairly wealthy early on, but at some point he hit a low point. By the time Shakespeare was becoming a man, his father was losing respectability and out of the town records, meaning that he no longer held office.
See the eNotes biography of Shakespeare, linked below. Here's what it says about his father:
His parents, John and Mary (Arden), were married about 1557; she was of the landed gentry, he a yeoman—a glover and commodities merchant. By 1568, John had risen through the ranks of town government and held the position of high bailiff, similar to mayor.
A glover is a glove maker. A commodities merchant is like a department store owner.