This has been the great debate for me lately.
My soon-to-be-completed first novel (post-college, at least) is written in the third person. I decided this would be a good idea because I wanted to utilize a few different points of view, such as seeing the world through the villain's eyes, and also through the two central heroes. However, I have had to constantly remind myself that I need to include some of the thoughts that belong to my characters. They think - so my reader can benefit from what they are pondering at certain moments. This has been coming easier as I've went along, but some good revision will help out the first half of the book, which is already finished a first draft and waiting for the ending to catch up.
I've recently picked up an intriguing YA dystopian novel called Matched, by Ally Condi, and I am really enjoying it so far. I have noticed that there is a trend that most of the YA books - many geared to young girls - follow, and that is to tell the story through a singular first-person POV. This viewpoint is always the central heroine to the story.
Investigating different books with this first person structure makes me itch to try it myself. My previous attempt at a first novel was started in the first person, and then I chickened out and second-guessed myself. That manuscript, part of an eventual series that's been planned since my high-school days, is sitting in my desk drawer right now waiting for me to brush it off and try again. I will eventually, once I finish the work on my current book.
They both have their strong points and stumbling blocks, but still, this seems to be a question I struggle with more and more: First or Third?