Is there a PDF reader that formats for mobile screens? Trying to read PDF on a mobile screen is a pain, be it iBooks or Adobe Reader. Neither of the apps properly format the content for reading on the iPhone. I was wondering if there is a "Reader" feature, similar to Safari's reading feature, on a PDF reading application that with a tap renders the content perfectly viewable on the tiny mobile screen. 

If there is no such application then I would like to know how I can convert a PDF into any other format that would allow me to format the contents better for viewing on the iPhone.
PDF files are popular precisely because the formatting is fixed. A PDF author can be sure that their document looks the same on any device that displays it. So I'm afraid you're asking for a feature that goes against one of the basic premises of the format.

That said, some PDFs have a text-only layer that can be displayed directly. On an iPhone, I'd recommend Goodreader for this. It will display the formatted PDF, then you can click to display the text-only version. That version may be bigger and more legible for you.

Having a text layer depends on the author of the PDF, but I would think Goodreader may be a step in the right direction for you.