Off the top of my head, actors who have done both comedy and serious roles and done both well (written with a total disregard of which genre came first)
Kevin Kline, Meryl Streep, Kevin Costner, Jerry Lewis, Dean Martin, William Shatner, Brad Pitt, George Clooney, Spencer Tracy, Alan Arkin, Henry Fonda, Jack Nicholson, Susan Sarandon, Tom Cruise, Nicolle Kidman, Matt Dillon, Dustin Hoffman, Ray Liotta, John Travolta, John Cusack, Ernest Borgnine, Andy Griffith, Jackie Gleason, George C. Scott, Tom Hanks, Woody Harrleson, John C. Riley, Burt Reynolds, Donald Sutherland, Gary Oldman, Tim Robbins, John Lithgow, Dennis Hopper, Renée Zellweger, David Schwimmer, Ian Mcshane, Christopher Lambert, Matthew Broderick, Colin Firth, Bette Midler, Whoopi Goldberg, Ted Danson, Michael Keaton, Sandra Bullock, Gérard Depardieu, Bob Hoskins, Kathleen Turner, Peter Falk, Bruce Willis....
along with a few hundred others I can't think of right now.