The medium that recieves the most re-inventions is clearly that of film but it's not exclusive.
Last year a re-make of Clash of the Titans was released, taking the basic plot of the 1981 version the remake adds and takes away details from the original such as taking away the "cheesy chessboard manipulation of characters" by the gods.
The overall design and feel of the film is much more updated to appeal to a younger generation, the production cast has cited as wanting to create a darker and more realistic tone, essentially updating an 1981 blockbuster into a 2010 blockbuster with the main differences being a re-imagination of the details and general aesthetic.
The Marvel Super Hero Squad original started of as a toyline based off Marvel's characters for ages 3+. The first immediate difference you can see is the cartoony style and general softening of characters and generally more child friendly aesthetic.
This re-imagining branched into a whole franchise including tv shows and video games that expanded the characters giving them much friendlier personalities and personifications with more of an emphasis on comedy aswell as adventure; for example Wolverine originally a tough as nails, quick to anger and violent character is presented in very much a watered down pastiche of himself.
This shows a radical change from an original IP and how it can be successful given the right circumstances.
The Legend of Zelda is a video game series in which the same basic story of a chosen hero in green is given the task of rescuing a princess from the hands of an evil wizard.
In total there are 14 Zelda games which tell this story in different ways such as changing details about the characters, in one game the hero is an orphaned forest child, in another he is the son of a farmer, but the result is always the same; good rises and evil is vanquished.
Along with details changing in each game so do the aesthetics, with each new technological advance the graphic style changes in the Zelda games, sometimes radically or sometimes subtlely.
The important thing to know is that each game is the same and different from the last making this series one of the most re-invented franchise in videos games, potentially in general entertainment.
When it comes to reinventions there have been numerous adapations of stories to suit other audiences, one such instance was the 2006 film The Departed. Based off the Hong Kong film "Infernal Affairs", the Americanised version keeps the same theme and general plot simply replacing them with American characters and settings. It's not the only time that a film from another country has been "Americanised", there has been other such as "Let Me In", adapted from "Let The Right One In", "The Ring", adapted from "Ringu". The list goes on but the point being that a re-imagination of an existing IP can merely change the locality.
One last re-invention to look at is the ancient tale of Journey to the West, telling the tale of the Monkey King. It's been adapted many times to different languages and different mediums, from tv to Stage to Music to even video games, each time taking on similar and different qualities. Most recently the story has been adapted for a video game that gives on a steam punk/futuristic aesthetic.
It's important to keep in mind that re-invention of an IP is not an uncommon thing and theres no limit to how you can change an already existing concept, you can change the target audience, the aesthetic, the details, the locality but people will still be able to see influences and origins of the original. It's important to be aware of the changes you're making whilst remembering the original.