It is a moment of typical repartee on the hit NBC comedy Cheers. Woody, surely the most befuddled bartender in the land, is standing in his workplace, laconically shooting the breeze with his colleague-in-pouring, Sam (Ted Danson), when an irresistible, short-skirted young woman flounces by. "Oh, my God, Woody, is it me or is that woman gorgeous?" asks Sam. Woody gets a look that, on him, passes for pensive. "You look nice, Sam," he says, supportively. "But I'll have to go with the woman."

The deadpan sincerity of actor Woody Harrelson—the first names are a coincidence—suggests a certain kinship with the dumb Woody he plays, and Harrelson claims there really are similarities. "There's a parallel between the natural simplicity of Woody and me," he insists. The comparison, however, is hardly apt. "Woody is not the naive, innocent, dumb joke he plays on TV," Danson says, and Harrelson has recently been demonstrating that his acting ranges beyond male bimbodom. He just finished a cameo in Casualties of War, starring Michael J. Fox and Sean Penn. He is currently starring at West Hollywood's Court Theatre in Edward Albee's Zoo Story and in Two on Two, a one-act play about friendship that he wrote. Yet the greatest difference between Harrelson and the affably dense bartender he portrays on TV has nothing to do with brains or performing. Despite his easy manner, Harrelson has known more than his share of personal violence, and he is even now coming to terms with a troubling, tragic family inheritance. In 1982 Woody's father, Charles, was convicted of conspiracy to commit murder and is serving a life sentence in Illinois.

Charles V. Harrelson, a previously convicted hit man, became an important figure for his son only seven years ago. When Woodrow Tracy Harrelson was 7, in 1968, his father vanished from their home in Houston, leaving his wife, Diane, now 51, to support Woody and his two brothers on her pay as, oddly, a legal secretary. In 1981, when Woody was a junior at Indiana's Hanover College, his father dramatically resurfaced: He was charged and eventually convicted in the shooting of John H. Wood Jr., a federal judge in San Antonio, whom he allegedly killed in a drug-related matter. Although the dealer who was accused of hiring him was acquitted on a retrial, Harrelson got life. Woody closely followed the trial of his father, whose birthday he shares, in the papers and calls the conviction "a travesty." He believes his father was a victim of prejudicial pretrial publicity and points out that the trial judge was one of the murdered man's pallbearers.

Woody denies that his anger over the proceedings stems from filial affection. "I don't feel he was much of a father," he says of the man he knew mainly through infrequent letters. "He took no valid part in my upbringing." Yet since Charles Harrelson's imprisonment, father and son have grown closer. Woody visits the prison once a year, and in 1987, when Charles got married by proxy (to a woman he had known on the outside), his son stood in for him. "This might sound odd to say about a convicted felon," Woody says, "but my father is one of the most articulate, well-read, charming people I've ever known. Still, I'm just now gauging whether he merits my loyalty or friendship. I look at him as someone who could be a friend more than someone who was a father."

As a boy, Woody exhibited the rage that is often found in abandoned kids. "I had a dichotomy about me," says Harrelson, who off-camera sounds more like a careful sociologist than a homey barkeep. "I had an unusual sensitivity but also an unearthly violence that just came out in spurts." Diagnosed as hyperactive, he was given the tranquilizer Ritalin, but the disturbances persisted: He was expelled from elementary school for kicking a teacher, fighting and breaking windows. In 1974 the family—his grandmother "Sweetie Pie" and great-grandmother Polly shared the house—moved to Lebanon, Ohio, and Woody vowed to fit in with his new peers. He joined the high school football team, and by that unusual route discovered a thirst for acting.

On the team bus after one game, Woody did an impromptu impersonation of Elvis Presley singing "All Shook Up." "Everybody applauded," he recalls. "I loved it. I don't care what actors say, it's the applause that does it." The rebel was instantly stage-struck. He started appearing in school plays, and in college, as a theater and English major, he landed leads in Li'l Abner and Cat on a Hot Tin Roof. Then he went to New York to be an actor. For a couple of years he performed as a waiter more often than as a thespian, but in 1984 he became an understudy in Broadway's Biloxi Blues and six months later was cast as a football player in Goldie Hawn's Wildcats. In 1985 he won his role on Cheers.

Woody the bartender has become one of TV's most beloved characters, and Woody Harrelson is doing well too. "He's one of the sweetest men I've met," says Brooke Shields, whom he dated briefly last spring. Observes Cheers co-star Kirstie Alley: "Woody has this little-boy quality that women find sexy. He's sexy because he doesn't know he's sexy. He'll come to the set after playing some sport and say, real innocently, 'Look at this scratch on my back.' Then he'll pull up his shirt and whoa! That body!"

Harrelson reacts to such encomiums ambiguously. "I don't think I'm really attractive to look at," he says. "But I would challenge anyone to have a conversation with me and not leave thinking, 'He's pretty damn great.' " So far, such lines haven't led to a lasting commitment. His 1½-year relationship with actress Carol (Taxi) Kane ended last fall, but her portrait hangs in his Big Bear home. "We had a friendship that became a romance and then a friendship again," he says.

As Cheers enters its seventh season, Woody is relishing the good life, California style: He commutes between his new three-bedroom beach house in Malibu, his apartment in Beverly Hills and his mountain cabin in Big Bear. He plans to play bartender for at least another year, but that is not his only occupation. Since 1986 he has been a partner in Son International, which sells such quirky items as circular beach towels and water-activated watches ("They work better on beer," he says). In the time left, he writes plays and indulges in long bouts with the novels of Nabokov and Faulkner.

Harrelson, still trying to figure out his father, does not plan to launch a family of his own soon. "I can't see myself getting nailed down for quite a while," he says. "I'm militantly single. I find it difficult to have sustained intimate relationships." Then the man who was abandoned at age 7 adds, "I'm not averse to a relationship where I can be vulnerable. As long as it doesn't entail exclusivity."