nginx
New to nginx? Read the nginx primer by Martin Fjordvald (external link).
I have been using nginx since 2010 now, and have grown to love it for a great deal of things.
nginx is not limited to the web; it can also natively load balance TCP/UDP streams amongst other things. I will recommend it for most use-cases. However, if you're currently using Apache and thinking of switching: First determine if you need to and whether you can do it easily (nginx has no .htaccess!).