This was a huge pain and I finally figured out how to solve it. I was working locally and whenever I tried to install a plugin WordPress would ask me for my FTP information. WTH (What the Heck!). I read a bunch of blogs with so-called solutions but none of them worked. I then found this simple blog which gave me the answer I needed (although I had to customize it a bit to work for my particular situation).
I stopped using MAMP on my mac and I have updated MySQL, PHP and Apache to run a virtual host. I like this solution better because MAMP never gets updated and I like having a virtual host because I can take control of the domain I am using. So after I browse to the directory that is hosting my site in the Terminal (following the instructions in the previous article), I note my username and group name and than I have to find out where the httpd.conf file is on mountain lion (versus where it is in the article (because they are using MAMP)).
You will find it here:
Use the Terminal to browse to that directory. Than open that file in a text editor and change this:
note: change the username to your username and group to your group
The last thing is to restart your server. You can do that in the terminal with this code:
[cc]sudo apachectl -k graceful[/cc]
This problem plagued me for a month. This solution finally got rid of the dreaded FTP permissions dialog that was popping up. Hope it helps you.