First person is a great way to make the reader really connect with the protagonist. If you, the writer, have a great character with a unique perspective on the world around him that just wouldn't come out in third person, then FP is the way to go.
I've read several books in FP that were done really well, like the Sookie Stackhouse books and the Dresden Files. Both protagonists are very different from the people they spend their time with, and while, in my opinion, Sookie Stackhouse could have been written in third person just as well as it was in first, I do think Harris did a great job with her series. (To be fair, I'm only up to the second book. So right now, the stories might have been DIFFERENT in third person, but not better or worse. I don't know how later books in the series turned out.)
The Dresden Files is an example of a series that would not have worked in TP. A lot of Dresden's personality comes through the narration, his inner thoughts, and sidebars to the reader. The books wouldn't be as engaging or entertaining in a different POV.
An example of a book that SHOULD have been written in FP but was written in TP instead? The Dexter books. The author wrote them as if he can see inside Dexter's head, but he tells the reader what's going on from the perspective of an observer, rather than letting Dexter tell the story himself. I believe the books would have been more engaging and I would be more sympathetic toward the protagonist if the books were written in FP.
So when you're getting ready to choose one POV over the other, ask yourself a couple questions: which perspective will make this book better? Will it enhance or get in the way of the story? and is the reader going to connect to the protagonist?