Eyeore reminds me of the importance of letting myself be melancholy sometimes. I spend a whole of energy trying to be upbeat and happy so that the people around me can feel comfortable. If my smile fades they want to know what's wrong. 99 of 100 times, nothing is wrong. It's okay to be melancholy sometimes.
Eeyore is my favorite. He doesn't want to be the center of attention, just remembered and included. I don't find him to be clinically depressed, but just authentic. I recently found how he got his name. The writer was trying to give him a name like a donkey sounds 'Hee Haw' and the R was supposed to be silent. So, initially it was to sound 'eey oh'.