Is every retelling of a character's story a re-imagining? In some ways yes, in some ways no. Every time a different group of people put on a play, they have different actors with different acting choices affecting the way the characters emote and interact with others; does that mean that every time a play is performed, that's a new interpretation? If so, then the characters in popular plays (particularly Shakespearean ones but let's not forget Peter Pan or Little Orphan Annie) are being constantly re-imagined. But, to me, that's a boring answer.
Does every cameo appearance of someone like Dracula count? To me, that's not very satisfying. He's appeared in serious movies, humorous movies, serious TV shows, humorous TV shows, serious comic books, humorous comic books, serious novels, humorous novels, etc. To say that the version of Dracula that met Abbot and Costello is some grand re-imagining... that feels a little weak to me.
For me, a re-imagining occurs when a character's story is different; not only do the minor details change, but the story itself is significantly different. And for that to happen, the character's story must be told, so minor appearances wouldn't count. That still leaves an awful lot of Robin Hoods and Tarzans. Wikipedia lists over 60 TV shows and films about Robin Hood, and that doesn't even count the cameos or ancient ballads.
But then, when we talk about comics, do we consider "alternate reality" tales to be re-imaginings? Batman... who is rarely reimagined in the actual comics canon... has been featured in many many "Elseworlds" and "Imaginary Stories". Do these count? Do I count the stories where Batman is a pirate or a Green Lantern or a cowboy or whatever? And then, there's the story where baby Kal-El is adopted by the Waynes and becomes Batman (with all the powers of Superman) when the Waynes are murdered. Is that a re-imagining of Superman or a re-imagining of Batman?