Here are a couple examples. (Keep in mind I haven't read all of these books, but the premise speaks for itself.)
Eragon
This is a little less shameless than most and mostly a product of a 16 year old writing it. I myself look back at the stories I wanted to write when I was a teenager and they were not all that original either. However this is worth noting.
Assuming that everyone reading this knows the plot of Star Wars see if this sounds familiar. A teenage boy was raised by his uncle on a farm. His uncle is killed in an attack from the empire around the same time that an old wise man finds the boy and teaches him about magical powers and tells him that he needs to defeat the evil empire. Also the old wise man dies in the first installment of the story.
If you can't tell which plot that synopsis is, the answer is both. Everything in that synopsis applies to both of these stories. Once again Paolini can't be blamed as he was a child when he wrote it, but still a note worthy example.
Percy Jackson and The Lightning Thief
While the plot on this one has its original aspects, the basic story seems to strangely reminiscent of everyone's favorite wizard.
"The protagonist is Percy Jackson, who discovers that he is the son of Poseidon, god of the sea. He learns that the legendary beings of Greek mythology still exist and have always existed, including monsters, cyclopes, empousae, Titans, and the Greek Gods" -Wikipedia
http://www.associatedcontent.com/article/2915776/a_review_and_summary_of_the_lightning.html
For those who have read Harry Potter this may sound somewhat familiar. Though the actual plot line follows its own course the basic premise is incredibly similar and such exploitations of a trend should not be ignored. However this is nothing compared to the next example.
Fallen
While I am not one to stand up for Twilight under any circumstances, this kind of blatant rip off is just ridiculous. Here is a plot synopsis that I found:
"Luce must spend her senior year at reform school... When she meets supernaturally gorgeous Daniel, she feels a familiar longing, making her believe they have met before. Although Cam is clearly interested in her, Luce only wants Daniel, who runs both hot and cold. He tries to keep Luce at a distance, telling her that the truth would kill her as it has many times before... Instead of vampires, though, these are fallen angels." -School Library Journal
In comparison to twilight:
"Bella's life changes when she moves to perpetually rain-soaked Forks, Washington. She is instantly drawn to a fellow student, Edward Cullen, beautiful beyond belief and angrily aloof. Bella senses there is more behind Edward's hostility, and in a plot that slowly and frighteningly unfolds, she learns that Edward and his family are vampires--though they do not hunt humans. Yet Edward cannot promise that his powerful attraction to Bella won't put in her in danger, or worse. Recklessly in love, Bella wants only to be with Edward..."
This is the most blatant rip-off I ever heard of. Stephanie Meyer wrote a book, it was a hit and became a best seller really fast, so naturally another author thought they could just jump on the train with the exact same story and make a quick buck. It is shameless and ridiculous.
So don't buy into the shameless rip offs. Find something original, there's enough of it out there. A story only needs to be told once. I don't want this to across though as a bash on anything that draws inspiration from anything else. If a writer can provide a new and interesting take on an old story that is excellent. The best example of this is the Lion King. It tells the story of Hamlet in a new and interesting way that makes it more accessible to everyone and not just those who understand Shakespeare, no easy feat.