lighttpd

Lighttpd (aka Lighty) is a lightweight webserver program with a small memory footprint. It is an alternative to Apache and IIS, which is particularly suited to systems which are low on resources, especially RAM. Lighttpd is ideal for people using VPS hosting. Even on hosts with plenty of resources, Lighty is apparently just as fast as Apache and sometimes faster, so is well worth considering.

Installation varies according to your platform, so check the instructions here.

You will also need to install php (maybe with an accelerator) as fast-cgi according to these instructions.

One notable difference between Lighttpd and Apache is the expires directive that controls the caching of content. Apache allows you to set the expiry by file type e.g. making a jpg images stay in the browser cache for a week. Lighttpd will only let you specify folders to be cached.