Woody hails from Hanover, Indiana, where he was voted the smartest student in school. He and his childhood sweetheart, Beth Curtis, were also voted "Couple Most Likely to Explode," as they were both obese at the time. It was later revealed that they always ate, to excess, around one another due to their palpable sexual tension.
Woody followed in Coach's footsteps in many ways, failing to understand the most obvious jokes, concepts, and situations. Woody was essentially a straight man for all of Cheers, though his humor stemmed from his misunderstandings. Woody once told Dr. Crane he was the smartest man he knew, excepting Cliff Clavin.
Woody seemed to have an off-center mentality, misunderstanding others' comments much as Coach had done. When Bill Medley of the Righteous Brothers appears and starts singing "You've Lost That Loving Feeling," Woody asks him, "How come you changed your name from Righteous?"
Woody arrived at Cheers expecting to meet his "penpal" Coach (with whom he exchanged pens, instead of letters). Upon learning of his death, he accepted the open bartender position. In the coming years he filled the void left by Coach, and eventually married the wealthy Kelly Gaines (Jackie Swanson), overcoming her father's objections to Woody's lowly station in life.
In the final season Frasier Crane orchestrated an experiment that went awry and resulted in Woody's election to the Boston City Council. He and Kelly were expecting their first child when Cheers ended. Frasier extrapolates on Woody's interest in a political career to the point that Woody becomes President of the United States and shows his displeasure with another country by using "The Bomb" (illustrated twice in Frasier's imagination as a mushroom cloud).
Woody would later make an appearance on Frasier, the spin-off show from Cheers, in which during a visit to Seattle he reconnected with Frasier Crane, who had since moved there from Boston. After a one-night reunion, the two began to spend a great deal of time with each other - which gradually turned into an ordeal for both, as they quickly realised they had moved on from their past and settled into new lives (with, ironically, neither man seeing the other's life as being particularly fulfilling). The two men decided to part company on good terms, after sharing a final drink with each other. Although not shown, this episode references Woody singing, "What Kind of Fool Am I?"
Woody's political career was not mentioned in Frasier. It is implied (though not directly stated) that Woody has returned to work at Cheers. Since Woody married into wealth, it is possible he returned to work to Cheers out of pleasure rather than a need for work.
On Frasier it is revealed in the episode The Show Where Sam Comes Back that Kelly and Woody's first child was a baby boy. In the episode The Show Where Woody Comes Back it is revealed that Kelly and Woody had another child, a girl.