He alternated with Jeff Bergman, Greg Burson, Jim Cummings, Bob Bergen, Maurice LaMarche and Billy West in voicing Warner Bros. cartoon characters such as Bugs Bunny, Daffy Duck, Porky Pig, Sylvester, Tweety, Elmer Fudd, Yosemite Sam, Foghorn Leghorn, Pepé Le Pew, Marvin the Martian, Speedy Gonzales, Wile E. Coyote, Road Runner and Taz, among many others.

Alaskey was the second actor to voice Grandpa Lou Pickles on the Nickelodeon cartoon Rugrats (taking over after David Doyle's death in 1997).

Alaskey was in several television shows including Night Court, Head of the Class, Back to the Future, and Spitting Image: The 1987 Movie Awards.

Alaskey was in the independent film The Legend of Sasquatch and voiced Mermaid Man in the video games SpongeBob SquarePants: Lights, Camera, Pants!

Alaskey played Beano Froelich in Out of This World but left the show early in its final season, making only infrequent appearances in a few episodes.

[citation needed] In 2003, he took over the roles of Bugs Bunny and Daffy Duck in the film Looney Tunes: Back in Action.

He answered questions and told his story, then went out onto Hollywood Boulevard and talked to people on the street who wanted to hear his famous voices.

[10] In 2014, Alaskey started narrating the television documentary series Murder Comes to Town, which airs on the Investigation Discovery Network.

Alaskey's only leading role in a live-action film was as lovable loser Ron Douglas in the black comedy Lucky Stiff, directed by Anthony Perkins and co-starring Donna Dixon and Jeff Kober.