Zaslow was born in Inglewood, California. He played Dick Hart on the CBS soap opera Search for Tomorrow and Dr. Peter Chernak on Love Is a Many Splendored Thing. He also played David Renaldi on ABC's One Life to Live from 1983 to 1986, and in 1998. Zaslow was also a writer for the NBC soap opera Another World.
Zaslow guest starred on a number of other television shows and soap operas, including Barnaby Jones and Law & Order. In the episode "The Man Trap," the series' September 8, 1966 premiere of Star Trek, he played Crewman Darnell, the first Starship Enterprise crew member to be killed off. The incident sparked the first diagnosis of the now-famous line: "He's dead, Jim," by Enterprise crew-member Dr. Leonard McCoy (DeForest Kelley). He also appeared as Jordan in the episode "I, Mudd". He also costarred in the 1977 feature film You Light Up My Life, and appeared in the 1979 sci-fi movie Meteor.
Zaslow's Broadway theatre credits included Fiddler on the Roof, Cat on a Hot Tin Roof, and Onward Victoria.
Zaslow was also the godfather of film and television actor Christian Slater.
However, it was for his work as Roger Thorpe on Guiding Light that Zaslow was always best known. One of the show's central villains of the 1970s, his first onscreen "death" was voted the top scene in the show's history when the series celebrated its 50th anniversary. In the late 1980s, he returned to the show and, once again, became a central figure. Zaslow received multiple Daytime Emmy nominations (and one win) for his work in the role and continually appeared on both critics' and fans' lists of favorite soap opera performers.
In 1997, he began to experience difficulty speaking. When it became noticeable on screen, he was placed on leave at Guiding Light. (There are conflicting stories as to whether Zaslow was then fired; there was for some time a legal action against Guiding Light and sponsor Procter & Gamble, which eventually was settled.) It was some time before Zaslow was finally diagnosed with amyotrophic lateral sclerosis (ALS), or Lou Gehrig's disease. (It was first thought he suffered a stroke). Zaslow did not return to Guiding Light and his role was briefly recast before being written off. (In 2004, Zaslow's character on Guiding Light died off-screen.)
Zaslow was hired at One Life to Live in 1998 to play David Renaldi again, appearing first in May of that year, his condition being written into the storyline. Zaslow made numerous appearances over the next seven months before he was too ill to continue working; his final appearance on One Life to Live was televised December 1, 1998, days before his death. His character was never killed off on the soap opera, which went through a series of writers over a two-year period, none of whom chose to deal with David's illness and Zaslow's death.
His widow, psychologist/writer Susan Hufford founded ZazAngels, a foundation that wishes to raise funds in order to find a cure for Lou Gehrig's disease. Several of his Guiding Light and One Life to Live castmates, along with many Broadway-based theater luminaries, have participated in tributes to Zaslow that were fundraisers for ZazAngels.
In 2004, Zaslow and Hufford's daughter Helena died. Susan Hufford released a book about Zaslow and his fight with ALS, titled Not That Man Anymore. Zaslow had begun writing the book several years earlier.
In 2006, Zaslow's widow Susan Hufford died from cancer. She is survived by her daughter, Marika Zaslow.