While the LAMP stack (Linux + Apache + MySQL + PHP) is very popular for powering WordPress, it is also possible to use Nginx. WordPress supports Nginx, and some large WordPress sites, such as WordPress.com, are powered by Nginx.
When talking about Nginx, it is important to know that there are multiple ways to implement Nginx. It can be setup as a reverse-proxy in front of Apache, which is a very powerful setup that allows you to use all of the features and power of Apache, while benefiting from the speed of Nginx. Most websites that report using Nginx as the server (based on stats gathered from HTTP response headers), are actually Apache running with Nginx as the reverse proxy. (The HTTP response headers showing “Nginx” are being reported by the reverse-proxy, not the server itself.)