The legal blog Lowering The Bar has a list of lawsuits where both the plaintiff and the defendant were the same person or legal entity.
Some of the examples are:
"Utah Court Says Woman Can Sue Herself", Lowering the Bar
You might not consider Utah the most progressive state, but it has become the first to grant its citizens a controversial right that many have long been denied, proving that the law does evolve. Utah has now become the first state to officially allow its citizens to sue themselves.
As the Salt Lake Tribune reports (thanks, Mark), a unanimous panel of the Court of Appeals ruled on February 15 that Utah law allows a decedent's heir and the personal representative of his estate to sue the driver who allegedly caused the accident that killed him. That wouldn't be unusual except that in Bagley v. Bagley, those are all the same people.
"Woman Seeks Damages for Damage Caused by Woman", Lowering the Bar
"I think I can safely say this is a very unusual claim," said Shari Moore, the city clerk of St. Paul, Minnesota. Moore was talking about Megan Campbell's claim against the city for damage to her car caused when a city vehicle crashed into it. Driving that city vehicle: Megan Campbell.
However, all of the lawsuits listed appeared to have been thrown out or in progress. There was also a recent report of a man suing himself and winning, but the article was sourced from a satirical news site.
Are there any examples of such cases of autolitigation where the plaintiff was awarded damages of some kind, as opposed to the lawsuit being thrown out?