In my particular case, I'm using nginx on a group of machines I inherited that are no longer running their own mail servers and all of our web traffic is either static or fastcgi. I had never used nginx before, and now I'm left with the decision of taking the effort to replace it with something I'm more familiar with or learning something new, but I don't know enough about it to know what benefits having it under my belt would hold.
I am currently using nginx on a single web server. It hosts mainly static content, some PHP, some Python, and some Ruby. The reason I chose it was for the lightness. I find it to use significantly less memory than Apache and I have had no problems with it thus far. My page load times have even decreased slightly.
I think the main benefit is the lightweight factor. If you are looking for a simple and clean web server, nginx offers a great option.
nginx usage in the Internet is increasing. It's a very lean and fast server, often used as a reverse proxy for e.g. load balancing, but it does a great job on its own. It has great community support and is actively developed by the original author.
I think it's worth to know this tool.
I can't recommend nginx enough, combined with php-fpm and xcache its excelled in performance compared to every other web server I've ever tried (Apache, IIS, Lighttpd). Extremely flexible, extremely fast, only downside is it takes a while to get setup.
We've been using nginx as a reverse proxy at work for a long time, and I've recently started using it for php and python projects at home. So +1, definitely worth knowing.
Things feel blazing fast, even on low-end hardware.
I use it due to it's light weight, but I keep Apache around to handle any pages that absolutely require it (such as those dependant on dynamically updated .htaccess files).
I found a nice way to share a PHP process between the two of them: see my answer at stackoverflow here: https://stackoverflow.com/questions/574690/sharing-php-cgi-between-apache-and-nginx