Unix and Linux are two of the most popular operating systems for Web servers. And these servers are some of the best available. I based my choices on security, cost, availability of support, and all around usability.
Apache is a free, fully configurable Web server available for Unix, Linux, Windows, Mac OS and other operating systems. It is one of the world's most popular Web servers and has many people working on improving it all the time. This server can be very difficult for the novice to install, but there are now companies that offer support plans and assistance to keep your sever up, running, and secure.
Zeus Web server is a highly scalable and secure Web server. It is recommended by people such as the Gartner group as a viable replacement for other less-secure Web servers. It can be a lot more expensive than Apache, but for the price, you get a lot of service and functionality.
iPlanet Web server is the latest offering from the people who brought you Netscape Web server. It is secure and offers flexibility such as Java Servlet capabilties and more. It is a very popular Web server for enterprises.
Roxen Web server is a free, open-source Web server similar in features to Apache. It offers many of the features that Apache offers, but it is primarily a tool to get you to buy other Roxen products. It has good integration with the Roxen site tools, but those are not cheap, and most of the advanced functionality of the server requires that you buy them.
AOLServer is a free Web server available for the Unix platform. It offers many of the same features as Apache, including database integration, built-in Tcl scripting, multi-threading capabilities, and it's easy to setup and use. It has no support for 128-bit encrypted SSL. It's not the most scalable server available, but it is fairly powerful.
Jigsaw is not a server meant for Enterprise level Web sites. But if you are interested in playing with the cutting edge technologies on your Web server, then this is the server to get. Jigsaw is a free, Java-based Web server with applet-based administration tools that make it easy to use. It is meant to showcase the latest technologies, and as such can be less stable than other commercial servers.