Shaughnessy first became widely known for playing Shane Donovan on the soap opera Days of Our Lives from 1984 to 1992. His character's romance with Patsy Pease's character, Kimberly Brady, made the duo into a soap supercouple and revived interest in Days among teenage viewers in the 1980s. In 1986, he appeared with Betty White and Bert Convy on Super Password, and in January 1993, Shaughnessy appeared in an episode of Murphy Brown as the title character's date to the inaugural ball.
Shaughnessy is also well known for his portrayal of Maxwell Sheffield opposite Fran Drescher on CBS' The Nanny from 1993 to 1999. He and Drescher resumed acting together in Drescher's next sitcom, Living with Fran, wherein Shaughnessy appeared fairly frequently as her philandering but needy ex-husband, Ted. Living with Fran was cancelled on 17 May 2006, after two seasons.
In 1996, Shaughnessy was reunited with another co-star from Days of Our Lives – Charlotte Ross, who portrayed Shane's daughter, Eve Donovan – for the TV movie A Kiss So Deadly. This time, Ross portrayed the roommate of Shaughnessy's daughter (Dedee Pfeiffer); Shaughnessy's character, although married, forms an obsessive Lolita-esque relationship with Ross. When she tries to break it off, Shaughnessy's character murders Ross' character; gradually, his daughter uncovers the truth.
Shaughnessy also appeared (in a dual role) in the Disney Channel 2002 made-for-TV movie Get a Clue. He was also seen in the 2000 made-for-TV Halloween movie Mom's Got a Date with a Vampire starring opposite Caroline Rhea; she guest-starred on The Nanny in 1998 as part of a cross-over with Hollywood Squares. That same year, Shaughnessy made two appearances on The WB's Sabrina (this show stars Rhea, Melissa Joan Hart, and Beth Broderick) playing two different characters. He played Alec Colson in the 8th-season episode "Covenant" of Stargate SG-1. He also voiced Dr. Quintaine in the PC game Freelancer.
Shaughnessy appeared on an episode of NBC's Law & Order: Special Victims Unit and is also the voice of Dennis the Goldfish on the Disney Channel cartoon series Stanley. On 11 May 2002, Shaughnessy won an Emmy Award for Outstanding Performer in an Animated Program for his portrayal of Dennis the Goldfish on Stanley.
On 8 August 2008, Shaughnessy portrayed the murder victim (Samuel, Guru) in Murder 101: The Locked Room Mystery. As of September 2008, his voice was heard in a few television commercials for Range Rover cars. In December 2008, he provided the voice of Pietro in The Tale of Despereaux. He also portrayed the Cockney English accent for "The Boss" in the game Saints Row 2, and more recently has voiced more commercials for Land Rover.
On 5 May 2009, Shaughnessy made a guest appearance in the series The Mentalist episode "Miss Red" as the manager of a private club. His voice has been featured in commercials for Land Rover. He also appeared on the popular TV show Hannah Montana as a talent show judge modelled after Simon Cowell in the episode "Judge Me Tender".
Shaughnessy returned to Days of Our Lives in May 2010, in a storyline associated with the funeral of Alice Horton (played by Frances Reid), briefly reuniting him with his former co-star Patsy Pease (Kimberly). This plot development was necessitated by the real-world death of the actress who had long portrayed Mrs. Horton, as the producers were aware that the audience would not accept the portrayal of the character by anyone else.
In August–September 2010, Shaughnessy appeared as King Arthur in Monty Python's Spamalot! at The Ogunquit Playhouse in Ogunquit, Maine. In January 2011, he won the Broadway World Boston Theater Award for Best Lead Actor in a Musical (Large Theater). Since 2010, Shaughnessy has starred on the soap opera web series The Bay as Elliot Sanders. On 6 December 2010, he reunited with Fran Drescher as a guest on her limited-run daytime show, The Fran Drescher Show.
In June 2011, Shaughnessy appeared as Henry Higgins in My Fair Lady at the North Shore Music Theatre in Beverly, Massachusetts. He made a guest appearance on the first-season finale of Fran Drescher's TV Land sitcom, Happily Divorced, first airing on 17 August 2011.
Shaughnessy returned to Days of Our Lives for a limited run in May 2012 as Shane Donovan, in a story line involving his return to the ISA and interacting with Hope and Bo Brady and Stefano DiMera. His co-star, Patsy Pease did not appear as Shane's wife, Kimberly, in this story arc; nor did Charlotte Ross, who had played Shane's daughter, Eve. He also returned in November 2013 for a three-episode arc, in which his character Shane, and his wife Kimberly, deal with their daughter's drug use.
On 23 January 2014, it was announced that Shaughnessy would assume the title role in the play Harvey at the New Theatre in Overland Park, Kansas after original star Judge Reinhold was offered the opportunity to leave the production.
In August 2014, Shaughnessy made a guest appearance on the Disney Channel show Dog with a Blog as business tycoon Tom Fairbanks, a man who wanted to buy Stan, the title character, and use him as the spokes-dog for his animal rescue campaign.