Actors/Actresses:
* Woody Allen (1935) - American actor, filmmaker, and comedian
* Rita Hayworth (1918-1987) - American actress
* Eli Wallach (1915-2014) - American actor
* Carly Rae Jepsen (1985) - Canadian singer, songwriter, and actress
* Danny McBride (1976) - American actor, comedian, and filmmaker
* Brittany Murphy (1977-2009) - American actress
* Billy Dee Williams (1937) - American actor
* Bruce Willis (1955) - American actor
* Jenny Slate (1982) - American actress and comedian
* Ben Stiller (1965) - American actor, comedian, and filmmaker
* Lucy Liu (1968) - American actress
* Diane Keaton (1946) - American actress
* Anna Kendrick (1985) - American actress and singer
* Justin Timberlake (1981) - American singer, songwriter, and actor
* Taylor Lautner (1992) - American actor
* Sarah Paulson (1974) - American actress
* Zooey Deschanel (1980) - American actress and singer
Musicians:
* Frank Sinatra (1915-1998) - American singer
* Stevie Nicks (1948) - American singer, songwriter, and guitarist
* Dolly Parton (1946) - American singer, songwriter, actress, and businesswoman
* Jimi Hendrix (1942-1970) - American guitarist, singer, and songwriter
* Ian Gillan (1945) - British singer, best known as the lead vocalist of Deep Purple
* Rita Ora (1990) - British singer, songwriter, and actress
* Miley Cyrus (1992) - American singer, songwriter, and actress
* Toni Braxton (1967) - American singer, songwriter, and actress
* Mary J. Blige (1971) - American singer, songwriter, and actress
Athletes:
* Wayne Gretzky (1961) - Canadian professional ice hockey player, often considered the greatest of all time
* Joe Namath (1943) - American former professional football player, known for his time with the New York Jets
Politicians:
* Richard Nixon (1913-1994) - 37th President of the United States
* John Kerry (1943) - American politician, 68th United States Secretary of State
Other:
* Mark Zuckerberg (1984) - American entrepreneur and founder of Facebook
* Walt Disney (1901-1966) - American entrepreneur, animator, voice actor, and film producer
* Bill Murray (1950) - American actor and comedian
This is not an exhaustive list. There are many other famous individuals born on December 1st, but this gives you a good starting point.