Unable to create directory wp-content/uploads/2013/04. Is its parent directory writable by the server?

Which user is nginx running under? Which group owns wp-content/uploads? What are the chmod permissions on wp-content/uploads?

not nginx expert but i think same as apache www-data
chmod your directory and you should be fine

I'm by far from an expert but this worked for me

chgrp nginx /var/www/wordpress/wp-content
sudo chown nginx /var/www/wordpress/wp-content

Also use this command to find out what user owns the nginx worker processes

ps -elf | grep nginx

In my above comment "nginx" was the name of the user who owned the process.

Hmm... this isn't working for me for some reason. Here is what I get with ps -elf | grep nginx:
$ ps -elf | grep nginx
55:1 S root 700 1 0 80 0 - 1501 rt_sig 20:24 ? 00:00:00 nginx: master process /usr/sbin/nginx -c /etc/nginx/nginx.conf
56:5 S www-data 702 700 0 80 0 - 1659 ep_pol 20:24 ? 00:00:00 nginx: worker process
72:0 S vagrant 874 32356 0 80 0 - 1156 pipe_w 20:33 pts/0 00:00:00 grep --color=auto -in nginx

I've tried everything - changing permissions and ownership so I can upload plugins and images to my WordPress install. I'm really not understanding why it's not working. Really frustrating!

@Jason: Try running

sudo chmod -R g+w /var/www/wordpress/wp-content

sudo chgrp www-data /var/www/wordpress/wp-content