TYPES OF WEBSERVER SOFTWARE

Apache web server - the HTTP web server

Free and the most popular web server in the world developed by the Apache Software Foundation. Apache web server is an open source software and can be installed and made to work on almost all operating systems including Linux, Unix, Windows, FreeBSD, Mac OS X and more. About 60% of the web server machines run the Apache web server - Refer Web server usage statistics from Netcraft.
Apache Web Server

Apache Tomcat

The Apache Tomcat has been developed to support servlets and JSP scripts. Though it can serve as a standalone server, Tomcat is generally used along with the popular Apache HTTP web server or any other web server. Apache Tomcat is free and open source and can run on different operating systems like Linux, Unix, Windows, Mac OS X, Free BSD.
Apache Tomcat
  
Microsoft's Internet Information Services (IIS) Windows Server

IIS Windows Web Server has been developed by the software giant, Microsoft. It offers higher levels of performance and security than its predecessors. It also comes with a good support from the company and is the second most popular server on the web.
Microsoft IIS Windows Web Server

 Nginx web server

Free open source popular web server including IMAP/POP3 proxy server. Hosting about 7.5% of all domains worldwide, Nginx is known for its high performance, stability, simple configuration and low resource usage. This web server doesn't use threads to handle requests rather a much more scalable event-driven architecture which uses small and predictable amounts of memory under load.
Nginx web server

lighttpd

ighttpd, pronounced "lighty" (don't ask me why), is a free web server distributed with the FreeBSD operating system. This open source web server is fast, secure and consumes much less CPU power. Lighttpd can also run on Windows, Mac OS X, Linux and Solaris operating systems.
lighttpd web server

Jigsaw

Jigsaw (W3C's Server) comes from the World Wide Web Consortium. It is open source and free and can run on various platforms like Linux, Unix, Windows, Mac OS X Free BSD etc. Jigsaw has been written in Java and can run CGI scripts and PHP programs.
The Jigsaw web server software from W3C

Klone

Klone, from KoanLogic Srl, includes a web server and an SDK for creating static and dynamic web sites. It is a web application development framework especially for embedded systems and appliances. No additional components are required when using Klone; thus, one can do away with an HTTP/S server or the active pages engine (PHP, Perl, ASP).
Klone web server

Abyss web server

Abyss compact web server runs on all popular platforms - Windows, Mac OS X, Linux and FreeBSD. The personal edition is (X1) 100% free while the professional Abyss Web Server X2 has a small price tag of $60. Supports HTTP/1.1, secure connections, CGI/FastCGI, custom error pages, password protection and much more. The server also has an automatic antihacking system and a multiligual remote web management interface.
Abyss web server

Oracle Web Tier

Includes two web server options with reverse proxy and caching solutions that lead to quick serving of web pages and easy handling of even the most demanding http traffic. The iPlanet Web Server, for example, is a high-performance server with enhanced security and mutithreaded architechture that scales well on modern 64-bit multiprocessors.
Oracle Web Tier
  
X5 (Xitami) web server

The cross-platform X5 from iMatrix Corporation is the latest generation web server using the company's own multithreading technology (Base2) that makes it scalable to multi cores. As per the iMatrix, X5 can handle thousands of connections without difficulty and thus is useful for long polling in which connections from clients remain open for extended durations.
X5 (formerly Xitami) web server

Zeus web server

The Zeus web server runs on Linux and Free BSD operating systems among others. It has been developed by Zeus technology Ltd. And is known for its speed, reliability, security and flexibility. The web server is used on some of the busiest web sites of the world including Ebay. Zeus web server is not free and costs more than a thousand pounds.
Zeus Technology Ltd. - Zeus web server

For further information, refer Web server comparison on Wikipedia