Possibility #5: Ahsoka Turns to the Dark Side
Evidence For: Ahsoka has, so far, displayed may traits similar to Anakin: recklessness, rebelliousness, strong attachments. Being Anakin's Padawan has only fueled these tendencies. Set off by the right tragedy, Ahsoka might fall to the Dark Side, foreshadowing her Master's downfall.
Evidence Against: Despite Ahsoka's flaws, there have been no hints, as with Anakin's character, of something deeply sinister yet to come. Her turning to the Dark Side would be too unexpected and unbelievable. And as always, one must return to the problem of her behavior's reflection on Anakin: surely his Padawan turning to the Dark Side very shortly before Revenge of the Sith would make the other Jedi more inclined to keep an eye on him.
Possibility #6: Ahsoka is Knighted
Evidence For: The Jedi are stretched thin during the Clone Wars. Anakin became a Knight without undergoing the customary trials. Perhaps a talented young Padawan such as Ahsoka might get pushed through to Knighthood earlier than usual in such circumstances.
Evidence Against: Remember that The Clone Wars takes place within a period of six months, and Ahsoka is only 14. Even if she'd been a Padawan for longer than a few months -- and even considering the show's young audience -- she'd be far too young to become a Knight. In fact, there are Padawans older and more experienced than her, such as Bariss Offee, who have yet to be Knighted.
In addition, training a Padawan to Knighthood is one of the biggest steps towards becoming a Jedi Master. If Ahsoka becomes a Knight, the Council would have little reason to deny Anakin the title of Master in Revenge of the Sith.
Possibility #7: Ahsoka Goes on a Mission
Evidence For: Sending Ahsoka away temporarily during Episode III would solve the problems associated with the more permanent ways of removing her. If she is sent off on her own mission at the end of The Clone Wars, that would work to show how her character has matured. Anakin doesn't mention her during Revenge of the Sith because nothing happened to her -- she's just away temporarily. In this scenario, perhaps she dies during Order 66 -- or perhaps she and goes into hiding, like with Obi-Wan, Dass Jennir, and a number of other Jedi.
Evidence Against: Dying off-screen during Order 66 would be an anticlimactic end for such an important The Clone Wars character. If she survives, though, there's plenty of future media to address what happened to her.
Possibility #8: The Clone Wars is a "What If?" Story
Evidence For: Here's where we get into some more bizarre, out-of-universe explanations for the events in The Clone Wars. If the series takes place in an alternate universe, perhaps in the real Star Wars universe, Ahsoka does not exist. To drive the "What If?" point home, perhaps something happens in The Clone Wars that prevents Anakin from falling to the Dark Side. If that happens, the series can continue past the time of Episode III without worrying about how to get rid of Ahsoka.
Evidence Against: There have been several "What If?" stories in Star Wars, published under the label Infinities. The Clone Wars has no such label, and as such it is considered canon. In fact, because of George Lucas' more direct involvement in the series than in other parts of the EU, it is considered a higher level of canon than the books, comics, and other media. With other stories referencing the characters and events of The Clone Wars, declaring the series AU would cause too much confusion in the timeline.
Possibility #9: The Clone Wars is an In-Universe Holodrama
Evidence For: Making The Clone Wars an in-universe story would clear up many discrepancies. Some of the series could be canon, because it's based on historical events, but other parts might be full of artistic license and other historical inaccuracies. Under this theory, perhaps Ahsoka doesn't really exist in the Star Wars universe, and she was invented to make the holodrama attract children; or perhaps her character is based on a minor, unimportant character whom Anakin temporarily trained. Timing matters less, too: consider M*A*S*H, where the Korean War lasted for eleven seasons.
Evidence Against: Although there is a precedent for EU works as in-universe documents, they are always clearly marked as such. Luke Skywalker and the Shadows of Mindor, for example, ends with a frame story where Luke Skywalker complains about the inaccuracies in the preceding tale. There are no such clues in The Clone Wars, and so suddenly declaring it in-universe fiction would be an unsatisfying cop-out.
That's not to mention the fact that, in the Star Wars universe, Anakin is remembered not for his heroism in the Clone Wars but for his atrocities as Darth Vader.No matter how much foreshadowing goes into The Clone Wars, an in-universe show featuring the heroic exploits of Darth Vader feels a bit like the Star Wars equivalent of Young Hitler's Adventures in Art School.
So What Really Happens to Ahsoka?
Fans have a long wait ahead before The Clone Wars ends and the writers reveal Ahsoka's final fate. No matter how the story ends, a great many people will inevitably be disappointed. Perhaps the best way for Ahsoka to go, however, would be a final confrontation with her former Master after he becomes Darth Vader. It will only show the extent of Anakin's transformation when he slaughters her mercilessly along with the rest of the Jedi.