The "Original" Timeline (Mostly):
This was the initial run of films before Days of Future Past hit the reset button.
X-Men (2000): Introduces Wolverine, Rogue, Professor X, Magneto, Jean Grey, Cyclops, Storm. Focuses on the X-Men forming to combat Magneto's Brotherhood.
X2: X-Men United (2003): The X-Men unite with Magneto against William Stryker. Further develops characters and their powers.
X-Men: The Last Stand (2006): Focuses on the "cure" for mutants and the Dark Phoenix Saga. Many characters die or are depowered.
X-Men Origins: Wolverine (2009): A prequel focusing on Wolverine's past, his Weapon X origins, and his relationship with Sabretooth. This film immediately starts creating major continuity issues with X-Men and X2 (e.g., Deadpool's portrayal).
The Wolverine (2013): Set after The Last Stand, focusing on Wolverine's time in Japan. This film ends with a post-credits scene setting up Days of Future Past.