According to Wikipedia, all of these fit that description:
- The Three Musketeers (1973) and The Four Musketeers (1974), shot as one film as far as the actors knew
- Superman (1978) and Superman II (1980)
- Trail of the Pink Panther (1982) and Curse of the Pink Panther (1983)
- King Solomon's Mines (1985) and Allan Quatermain and the Lost City of Gold(1986)
- Sleepaway Camp II: Unhappy Campers (1988) and III: Teenage Wasteland (1989)
- Jean de Florette (1986) and Manon Des Sources (1986)
- Back to the Future Part II (1989) and Part III (1990)
- Critters 3 (1991) and 4 (1991)
- The Three Colours Trilogy: Blue (1993), White (1994) and Red (1994)
- Blue in the Face (1995) was conceived and filmed completely ad libbed immediately following production of Smoke (1995)
- The Lord of the Rings: The Fellowship of the Ring (2001), The Two Towers (2002) and The Return of the King (2003)
- The Matrix Reloaded (2003) and The Matrix Revolutions (2003)
- Kill Bill Volume 1 (2003) and Volume 2 (2004), which were originally shot as one film and later edited into two
- Anchorman: The Legend of Ron Burgundy and Wake Up, Ron Burgundy: The Lost Movie (2004), the second being a DTV effort assembled from deleted scenes and outtakes of the first
- Ginger Snaps: Unleashed (2004) and Ginger Snaps Back (2005)
- Pirates of the Caribbean: Dead Man's Chest (2006) and At World's End (2007)
- Flags of Our Fathers (2006) and Letters From Iwo Jima (2006)
- Che: The Argentine and Che: Guerrilla (2008)
- Arthur et la vengeance de Maltazard (2009) and Arthur 3 : La Guerre des deux mondes (2010), which were edited into Arthur and the Great Adventure (2010) for release in the United Kingdom
- Harry Potter and the Deathly Hallows – Part 1 (2010) and Harry Potter and the Deathly Hallows – Part 2 (2011)
- The Twilight Saga: Breaking Dawn Part I (2011) and Part II (2012)
- Skyline "Skyline 2" (2013) and "Skyline 3" (2014)
Though not shot entirely back-to-back, the final scene of Star Wars Episode III: Revenge of the Sith was shot in Tunisia during the production of Star Wars Episode II: Attack of the Clones in order to avoid another trip to Tunisia for a single scene.
So maybe I can change my vote so we can preserve Star Wars episodes II and III!!! I know you all agree with me here!