Fisher, one of the squinterns on the TV show Bones is an Eeyore.
Most of his lines involve death, misery, and dying and he states that he is jealous of the corpses they work with. After the timeskip between seasons 5 and 6, it is revealed that he spent a year in a mental hospital for being too depressed to do anything but sleep 20 hours a day. Even Cam goes out of her way to try to get him to smile.
Debbie Downer (Rachel Dratch) from Saturday Night Live is an Eeyore.
Her theme song says it all:
You're enjoying your day
Everything's going your way
Then along comes Debbie Downer
Always there to tell you 'bout a new disease
A car accident or killer bees
You'll beg her to spare you
"Debbie, please!"
But you can't stop Debbie Downer!
Ringo Starr in the Beatles movie A Hard Day's Night is an Eeyore.
Apparently, he had shades of this in reality as well, but it did bother him when the press began referring to him as "the Sad Beatle" after the movie came out; he claimed that he was perfectly happy, but didn't have a naturally smiley face.
In Winnie the Pooh movies, Eeyore is depicted a clinically depressed character, but he is still loved unconditionally and taken care of by his friends.
Depression is a terrible disease and the movies taught kids to never leave behind a struggling friend.
Technically speaking, Eeyore most likely suffers from Dysthymia.
Sometimes referred to as Chronic Depression, a characteristic trait of Dysthymia is a depressed feeling or mood occurring most of the time. Like Eeyore, someone suffering from Dysthymia is almost always 'down in the dumps.' Because of the long-term nature of Dysthymia, individuals suffering from Dysthymic Disorder often neglect to seek treatment; depression is all these individuals have ever known, so to them it seems normal.