Apache is the most common web server. It is free and Open Source. The vast majority of commonly-used web content management systems (like WordPress, Drupal, and Joomla) and other similar applications are written primarily with Apache in mind.
Within a Linux environment, there are two major competitors to Apache, but they each have their own cost associated with them:
LiteSpeed is the easiest replacement for Apache. It provides faster performance and better scaling, and it acts as a “drop in” replacement — which means that it (essentially) works the same as Apache. Anything that is compatible with Apache will be compatible with LiteSpeed, and the configuration settings should be mostly identical. However, LiteSpeed is proprietary software, so you have to pay for it.
The other popular alternative is Nginx. Nginx is faster than Apache, especially when serving static files or cached files, and can be made to be as fast (or faster) than Apache for interpreting PHP and other languages. Nginx is also free and Open Source, which makes it comparable to Apache from a financial standpoint. However, Nginx doesn’t work the same way the Apache does. There is no guarantee of compatibility. Even when things are compatible, it can be difficult to find information — for example, it is possible to run WordPress with Nginx, but all the official tutorials and support documents assume you’ll be using Apache.
Apache also runs on Windows, but most people running Windows server will use IIS, which is Microsoft’s proprietary web server.
Some web applications and development frameworks, such as Ruby on Rails, have a built-in web server, and don’t require a separate web server.