Who was the author of this [approximate] quotation: "All the world is mad but me and thee, and I think I have doubts about thee?"

"All the world is queer save thee and me, and even thou art a little queer." --Robert Owen, 1828

I've found several variations. This article simply credits a Yorkshireman.

It was the Yorkshireman who said to his friend "Everyone in the world is quite mad, except for me and thee. And sometimes I have my doubts about thee."

http://www.fawlty-towers.com/complaints.htm

I found that page too, McGruff. In that form I can't find the quote definitely attributed to anyone. I think the Yorkshire attribution comes from that being about the only place the formal "thee" is still used, now that even American Quakers had given up the practice by WWI. The substitution of 'mad for 'queer' is self-explanatory, I think.
Here are a few places crediting Robert Owen:

http://www.goodreads.com/quotes/128546-all-the-world-is-queer-save-thee-and-me-and

http://www.quotes.net/quote/39904

http://10bestquotes.com/robert-owen-quotes/