Google PageSpeed has been one of the most impressive tools that you can use to boost the speed of your website without diving into the source code.
Google has offered a free module for Apache servers for 3 years now. Today, they have released an official module for Nginx servers.
I have personally used the Apache module and it is crazy good. You can notice the improvements within seconds. The kind of capabilities it offer is insane. If you run your own web server powered by Apache or Nginx, you should definitely check it out.