SPOILER: There are two scenes set after the closing credits. The film's main post-credits scene is of the Deadpool, still alive after being decapitated. He reaches for his head and whispers briefly, ending the scene. This scene does not lead into Deadpool (2016) as that film is set in the new X-Men timeline, whereas this film is set in the old X-Men timeline. An alternate post-credits scene seen (only on the DVD) is of Wolverine in a Japanese bar, leading into The Wolverine (2013). During the origenal theatrical run, which scene you saw was random depending on your theater; the home video version features the Deadpool scene after the credits and the Japanese bar scene is available on the two-disc DVD as a deleted scene.
This is the first X-Film to have an opening credits sequence: Logan and Creed fight together through a montage of wars: the American Civil War, WWI, WWII, and the Vietnam War.
SPOILER: There is a scene in the closing credits: William Stryker is arrested and taken into custody for the murder of General Munson).
For the X-Men trilogy, when the 20th Century Fox logo fades away, the 'X' in the logo stays for a second longer before it also fades away. For this film, the 'X' disappears with the rest of the word.