James Howlett was born in the 19th century and learned he had claws on each hand. He later participated in several wars.
X-Men: First Class
He appeared in a cameo where he says to Charles Xavier and Magneto "Go fuck yourself".
Logan
In the year 2029, Logan retired from being an X-Man and decided to be a cab driver.
References in other works
Hugh Jackman was supposed to make a cameo as Wolverine in 2002's Spider-Man, but the crew couldn't find his X-Men suit.
Wolverine's face appears in the extended cut of 2005's Fantastic Four.
In 2006's Flushed Away, Roddy (voiced by Jackman) checks his wardrobe and one of his outfits is a Wolverine costume.
Wolverine and Hugh Jackman get mentioned constantly by Deadpool in the 2016 movie Deadpool.
Archival footage of Hugh Jackman as Logan from X-Men Origins: Wolverine appears in the mid-credits scene of the 2018 movie Deadpool 2 where Deadpool kills his mouthless self to "clean the timeline".
Reception
Hugh Jackman's performance of Wolverine has been well-liked since the first movie.