Molly, don't read this, silly girl!! Wait until you've finished.
I'm quite certain this has been brought up before, but I cannot resist writing it again with the new HBP fodder we've been given.
Both JKR and George Lucas have been using Joseph Campbell's "Hero's Journey" method of storytelling. Star Wars has even been taught in English classes because it follows the model so closely. So, since Harry Potter follows the same structure, roughly, there are plently of similarities between Star Wars and Harry Potter.
Obi-Wan thought he could teach Anakin, but failed. He was the one who brought Anakin into the Jedi ways. Similarly, Dumbledore brought Tom Riddle into the wizarding world, fully knowing that he had darkness within, but thought that he could prevent it from fully taking hold.
They both failed, and both turned out to be the most feared villains, both who changed/had their names changed to reflect their new 'evil status.'
In both stories, both Tom Riddle/Voldemort and Anakin/Vader became physically deformed because of their pursuits. Anakin has an unfortunate run in with some lava, and Tom Riddle ends up destroyed his sexy, handsome self in the creation of Horcruxes.
Now here comes Harry. Although, no, Voldemort isn't Harry's father (I doubt that would come to pass considering how many comments there has been about the similar appearance of James and Harry, so much that even Harry says to shut it in HBP), Harry, too was living in the Muggle world (ordinary world, per Joseph Campbell's "Hero's Journey" story structure), ignorant of the fact that there were such things as wizards, though he knew he could make things happen and couldn't explain them.
Dumbledore brings Harry to Hogwarts, after stowing him away at the Dursley's, much like how Obi-Wan hid Luke Skywalker at his uncle's farm, only to later explain how Luke can be a Jedi, and Obi-Wan will teach him. Both Harry and Luke are considerably talented for their lack of experience in the magical/jedi world.
Of course, also following Joseph Campbell, then we have the inevitability that the hero must go on without his/her mentor. In both Star Wars and HBP, the two mentors voluntarily sacrifice their lives at the hand of the 'villians.' Obi-Wan allows Vader to kill him while Luke watches, and Dumbledore allows Snape to kill him while Harry watches (literally frozen).
And then... well, Obi-Wan manifests himself as some sort of spirit to Luke... I think we haven't seen the last of Dumbledore. We have the possibility that Dumbledore will be in his portrait, giving advice. The portraits appear to be independent spirits/thinkers that have their memories from life and the ability to continue on in the painting world.
Finally, Obi-Wan tells Luke that only Luke can destroy Vader-- that he has to fight him. While Luke has the concern that he can't kill his father, Harry doesn't have that concern-- but he does have the prophecy that Dumbledore imparts to him. Harry is probably the only one that can get rid of Voldemort, however the stakes for Harry is that if he doesn't, Voldemort is going to kill him instead-- that one cannot live while the other is alive.
Those are the parallels I can determine thus far. Any others you can think of?