1. Bringing Up Baby (1938)
2. In Name Only (1939)
3. The Philadelphia Story (1940)
4. Once Upon a Honeymoon (1942)
5. Arsenic and Old Lace (1944)
6. Notorious (1946)
7. Mr. Blandings Builds His Dream House (1948)
8. Operation Petticoat (1959)
9. Monkey Business (1952)
10. Father Goose (1964)Honorable Mentions: the rest of his films ;) jk. Gunga Din (1939), My Favorite Wife (1940), The Bishop's Wife (1947), Every Girl Should Be Married (1948), I Was a Male War Bride (1949), and Charade (1963).
UPDATE: Need to squeeze Mr. Lucky (1943) in here somewhere...
A few days ago I made a list of Cary Grant films that I haven't seen and there wasn't many (of the ones after he became famous). Out of the films he made before Topper (1937) I've only see Suzy (1936) and I will be watching Sinners in the Sun (1932) for the Hot and Bothered Blogathon.