Sean Bean, apart from his most edifying name (non-canonical variants: Shawn Bhawn / Seen Been), is probably the one modern actor who dies at the end of a great many films he has appeared in, whether as a protagonist, antagonist, tragic hero, megalomaniac or just a regular man. His only notable competition is John Hurt, whose on-screen characters also die with alarming frequency—in fact, Hurt's 43 on-screen deaths (prior to his real-life death in 2017) top the list—Bela Lugosi (35) and Vincent Price (33) both have quite a jump on Sean's 25-or-so deaths through the year 2020.
The frequency with which he has been killed onscreen has not been lost on the internet meme scene; for example, when actor James Purefoy was doing a Reddit AMA a year or so ago, he was promoting a new film he was appearing in called Wicked Blood (which, unfortunately, ended up being released straight-to-video). One of the first questions from the Reddit peanut gallery was "So, I see that Sean Bean is in your new movie. How does he die?"
The following is a list of Sean Bean's on-screen deaths, listed chronologically along with the cause of his character's demise. I should probably mention that reading the list below may spoil some of his movies for you, but then, it's Sean Bean. How else do you expect his films to end?
The Many Deaths of Sean Bean
If this list seems incomplete, try Cinemorgue (for the full list).
I've a strong feeling that we haven't seen the last of Sean Bean dying on-screen. Watch this space as I catalogue his various deaths. Note that about in about a third of the films listed above, his characters die by being shot. I'll go ahead and chalk this up to uncreative screenwriters.
Don't get me wrong. Sean Bean is a fine actor. He just seems to be cast in a whole lot of roles where he's playing a doomed character, possibly approaching the death numbers that career stunt performers have achieved on-screen, which is no mean feat for an actor who by and large doesn't do his own stunts. But that's Hollywood!... or Pinewood Studios.
Update 2019: Sean Bean has apparently had enough of being a meme! He stated in September 2019 that he'll no longer accept roles in which his character is destined for the wrong end of some deadly weapon following a campaign on Twitter in which the hashtag #DontKillSeanBean made quite the rounds. BoredPanda has the story.