The Twilight movies should be watched in the following order, which corresponds to their release and chronological storyline:

1. Twilight (2008)
2. The Twilight Saga: New Moon (2009)
3. The Twilight Saga: Eclipse (2010)
4. The Twilight Saga: Breaking Dawn – Part 1 (2011)
5. The Twilight Saga: Breaking Dawn – Part 2 (2012)

This order follows the progression of the story from Bella Swan meeting Edward Cullen through the saga's conclusion, including the two-part finale of Breaking Dawn