While trying to configure Nginx and PHP so that the PHP files would run from the same directory as static files, the error "290 rewrite or internal redirection cycle while internally redirecting to "/index.php"..." persistently recurred.

Everything worked fine after changing nginx.conf to the following (inside server {):

root html;
index  index.php index.html index.htm;
location / {
  try_files      $uri $uri/ /index.php?$args;
}
location ~ \.php$ {
  include fastcgi_params;
  fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
  fastcgi_pass   127.0.0.1:9123;
}

Source (in the "Also Good Section")