Curry's first role was in the 1991 feature film Talkin' Dirty After Dark where he appeared alongside Martin Lawrence.
Curry's first major role was on the ABC sitcom Hangin' with Mr. Cooper which made its debut in September 1992. On the show he played the lead role of Mark Cooper, an NBA player-turned-substitute teacher/gym coach. Hangin' with Mr. Cooper was eventually on air for five seasons with over a hundred episodes.
In 1994 Curry guest starred on the sitcom Living Single. In 1997, he made another guest appearance on the sitcom Martin. Curry was later featured on two episodes of The Jamie Foxx Show as eccentric driving instructor Sergeant Easy.
Curry also made cameos in the 1997 feature film Switchback and 1998 feature film Armageddon.
In 2000, Curry had a recurring role on The Drew Carey Show as Robert Soulard, Drew Carey's boss.That year he also hosted the Comedy Central game show Don't Forget Your Toothbrush and made a guest appearance on the sitcom For Your Love with his Hangin' with Mr. Cooper co-star, Holly Robinson Peete.
Curry went on to play the lead role of scientist Norton Ballard in the Disney Channel Original Movie The Poof Point. The movie reunited Curry with Hangin' with Mr. Cooper co-star Dawnn Lewis, who played the his onscreen wife Marigold.
Curry was the host of the PAX-TV show Animal Tails and BET's Coming to the Stage in 2003. In 2004, he appeared on Celebrity Mole Yucatan. He came in second place to Dennis Rodman.
In 2005, Curry was featured on an episode of Less Than Perfect and guest starred as Max Cooper on two episodes of Fat Actress. Curry made another guest appearance on a 2008 episode of the sitcom House of Payne. On November 30, 2008, Curry performed a stand-up comedy routine on The Comedy Festival Laffapalooza Special, hosted by Tracy Morgan.
From 2009 to 2011, Curry hosted Jamie Foxx's FoxxHole Live every Monday in the Conga Room in Los Angeles, which was heard on satellite radio stations Sirius 106/XM 149. In 2012, Curry joined Sommore, Earthquake, Bruce Bruce and Tony Rock on the Royal Comedy Tour.
He later appeared on two episodes of The Secret Life of the American Teenager.Curry also starred in Nick At Nite's first-ever original live-action family sitcom, See Dad Run, which debuted in 2012, as Marcus, who's a friend of Scott Baio's character. See Dad Run eventually ran for three seasons on the network.
In 2014, Curry joined Sommore's Standing Ovation Comedy Tour along with Bill Bellamy, Tommy Davidson, and others. That same year, Bounce TV launched the sitcom One Love, starring Curry and Sheryl Lee Ralph. In 2018, Curry was a special guest on the Katt Williams 11:11 Tour. Since 2018, Curry has also regularly performed stand-up comedy at the Hollywood Improv.