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.
There are a PILE of webservers out there. I expect depends on the usage you want. Apache will do most of what people want, it's known good, well updated, and will run on nearly any hardware and operating system combination.

For a comparison of web servers, check [Comparison of web server software](http://en.wikipedia.org/wiki/Comparison_of_web_server_software).