Tom Hanks kind of did it with Private Ryan. Although I put him in the category below.
Usually the comedians go for the drama. Jim Carey - Truman Show, Bill Murry - Lost in Translation, Steve Martin a few times that I am now forgetting, Adam Sandler in a few movies, Ben Stiller in Permanent Midnight and others, Robin Williams on multiple occasions, and Hanks as said above.
My pet theory is comedians start out as people who want attention (middle child syndrome?) and get it from being funny. Then they reach a point in life where they want to be taken seriously so they go for Oscars etc. The serious actors already were taken seriously so they go for fun, relatively easy work of action or comedy - DeNiro (analyze this), Nielson, Bridges, Neeson, etc.