The Anubis Gates by Tim Powers contains many examples. Great book.
The protagonist is an expert on the works of a particular poet. He travels back in time, and accidentally becomes that poet, writing his poems from memory. So who wrote the poems originally?
Thrice Upon a Time centers upon the invention of a device which allows communication into the past; with two major limitations. It requires a receiver, and it unmakes the future the message is sent from. It is used to stop a plague, and used to warn against turning on an experimental fusion plant *; in both cases resulting in different futures.
It’s windy and rainy here, and my cat just walked me around the house to make me open every door. Just to make sure that there wasn’t a door that led to Summer.
Been there, done that.
My understanding of this is: in the original, unaltered timeline, Judgement Day takes place in 2004. The events of the first movie, leading to the chip and arm being used to help develop the technology, moved the date up to 1997; but then the events of the second movie place the timeline back on track. Thus Judgement Day was, in fact, always going to happen.
The only problem with this theory is that Reese gave Sarah the 1997 date, before he died, which happened before the timeline was altered (I think. Been awhile since I’ve seen the first one). But I’m sure this could be explained away somehow. 
I feel guilty mentioning it in the same thread as some of the above nominations, but The Matrix made use of something like this - the Oracle’s spoken prognistications brought about the things she had foreknown. (although in some cases, her prognostication was the calculated opposite of what she saw happening, because it was necessary to say the opposite of what would happen in order to make it happen)
A recent story called “The Merchant and the Alchemist’s Gate” (a really excellent story IMO) has some of thstuff kind of like what’s described in the OP. For example
One character visits his future self, finds his future self in posession of a huge amount of money just sitting in a box, and takes the box of money back into the past. Hey, you can’t steal from yourself, can you? Anyway, he blows it all, then spends the rest of life saving up money to put into the box.
That’s if I’m remembering the plot correctly.
R. A. Lafferty’s “Rainbird.”
Harrison Rainbird is a super inventor of the 19th century. He invents a time machine to go back and give advice to himself on how to avoid dead ends. The next version of him goes on to even greater achievements, but still want to do more. He invents the time machine to advise himself again, but this time his younger self would much rather go hawking and none of Rainbird’s inventions are ever created, including the time machine he used to talk to himself.
RealityChuck, that sounds more like a self-destroying future than a self-creating one.
The grandaddy of all these is the story of Moses in the bible.
Pharaoh is told that a leader is about to be born to lead the Jews out of slavery. To prevent this he orders that all Jewish males born be cast into the river. Moses is born and his mother puts him in a basket in the river. Pharaoh’s daughter finds Moses and she raises him in the palace. This puts Moses in a unique position to free his birth people.
If Pharaoh had not listened to the prophecy, Moses would have just been another male slave. Pharaoh listening to the prophecy is what made it come true.
Well, there’s always Oedipus Rex in that case, too.
The episode “Ouroboros”?
And the Star Trek: The Next Generation two part story “Time’s Arrow”. The crew go back in time to save the future, because they’ve already been back from the future to save the future and told their future selves to do so. From the past.
Although, Marty was actually trying to repair the timeline he had screwed up when he gave his father more confidence. It should have been his father that fell out of the tree and got hit by his father-in-law.