Nginx is a web server which can also be used as a reverse proxy, load balancer and HTTP cache.
Nginx is free and open source software, released under the terms of a BSD-like license. A large fraction of web servers use NGINX, often as a load balancer.
NGINX relies on an asynchronous event-driven architecture to help power its goal of handling massive concurrent sessions. It has become a very popular web server among administrators due to its light resource utilization and its ability to scale easily.
Apache HTTP Server
The Apache HTTP Server—often referred to as httpd, or simply Apache—was first launched in 1995, and celebrated its 20th birthday in February 2015. Apache powers 52% of all websites globally, and is by far the most popular web server.
While Apache httpd is most often seen running on Linux, you can also deploy Apache on OS X and Windows. Apache is, unsurprisingly, licensed under the Apache License version 2. The web server itself uses a modular architecture, in which extra modules can be loaded to extend its features. For example, loading the mod_proxy will allow for a proxy/gateway on your server, and mod_proxy_balancer will enable load balancing for all supported protocols. As of version 2.4, Apache also supports HTTP/2 through a new module, mod_http2.
Apache Tomcat is an open source Java servlet container that functions as a web server. A Java servlet is a Java program that extends the capabilities of a server. Although servlets can respond to any types of requests, they most commonly implement applications hosted on Web servers. Such web servlets are the Java counterpart to other dynamic web content technologies such as PHP and ASP.NET. Tomcat’s code base was donated by Sun Microsystems to the Apache Software Foundation in 1999, and became a top-level Apache project in 2005. It currently powers just under 1% of all websites.
Apache Tomcat, released under the Apache License version 2, is typically used to run Java applications. It can, however, be extended with Coyote, to also perform the role of a normal web server that serves local files as HTTP documents. More information can be found on the project website.
Apache Tomcat is often listed among other open source Java application servers. Some examples are JBoss, Wildfly, and Glassfish.
Lighttpd—pronounced “lightly”—saw its initial release in March 2003. It currently powers approximately 0.1% of all websites and is distributed under a BSD license.
Lighttpd distinguishes itself with its low memory footprint, small CPU load, and speed optimizations. It uses an event-driven architecture, is optimized for a large number of parallel connections, and supports FastCGI, SCGI, Auth, Output-compression, URL-rewriting and many more features. Lighttpd is a popular web server for the Catalyst and Ruby on Rails web frameworks. Find more information on the project homepage.
If you are looking to try one of the popular web servers, I can highly recommend downloading a LAMP (Linux, Apache, MySQL, PHP) or LEMP (Linux, NGINX, MySQL, PHP) stack. There are plenty of such stacks available, providing different flavors in for example Apache and PHP versions. They are usually provided as one-click installers, or available in your package/software manager on Linux.