It is amazing to me that anyone would recommend setting file permissions on the "world" access section of any internet accessible directory (last 3 bits (******rwx--final "7" of the 777 attribute) to 7, making that directory and all its subdirectories world-readable, writable AND executable! You should never have to do this. The maximum permissions these directories require is 755 if ownership of these directories is set properly.
What is confusing most people about this is that these directories, when set to the proper 755 must be writable by the owner of the web server process that is running on the installed NIX system. You need to change the owner of these directories to be the owner of that webserver process (usually "chown -R apache:apache wp-content") on most Linux systems.
However, you can temporarily set your permissions on these directories to 777, create content in them, and then check the ownership of the directories and files that were just created within these directories to determine what user created them--e.g. "ls -l" from within the directory that was just created via the WordPress interface--directories and content within the wp-content directory.
Once you have identified this, change the permissions on the wp-content back to 755 and do a recursive change for the ownership and permisions on that directory--e.g. "chown -R <webserviceuser>:<webserviceuser> wp-content" and "chmod -R 755 wp-content"
If you are hosting WordPress on some provider that does not allow you to change this ownership appropriately in this fashion on your own, you should contact them to have perform these proper security steps. If they will not (it's not a matter of "can do"), then be prepared to have your content, themes, et.al. hacked. Because if you leave these directories set to 777, any joe-hacker with a minimum of skills will be able to hack your WordPress site and content. In such a scenario, it would be wise to get yourself a different ISP for hosting your site.
Senior Systems Engineer
Bravo Systems Technologies
"Advanced Open Source Solutions for Business"
Chicago, IL USA