Question: I've traditionally deployed my sites under apache, simply by default. I've heard things about NGinX though and I'm wondering under which conditions it would be superior. In addition to apache and Nginx, what the other options are for webservers and what are their benefits?

Answer: 
Yes.

One of the web servers used to have a large spike in load every few hours. After looking into the logs, I found out when the load spike happened, there where a lot of people looking at the gallery. 

So I off-loaded 99% of the static content from apache to nginx. apache was left to serve all of the php. The load on my web servers dropped to a nice low number and with no more high load spikes.

If you are looking to get more out of your servers, definitely have some light-weight server serve all the static content.
[Netcraft](http://netcraft.com/) tracks market share of web servers & according to them, IIS stands second after Apache with a 26.03% share (as of July 2010). This is based on a survey of 205+ million sites

[This link](http://blogs.iis.net/bills/archive/2007/05/07/iis-vs-apache.aspx) has reasons why you should check out IIS7 if you use Apache today