http://cherokee-project.com/ and http://www.lighttpd.net/ are the only other ones I've heard of, and they seem to have their own niche they target. There is also https://github.com/okws/okws. I'm sure there are many more, but none of them have sizable market share, especially compared to nginx/apache.

HAProxy[0] has fit the bill for me in many instances.

[0] http://haproxy.1wt.eu/

Just want to mention that HAProxy isn't a web server like nginx, but a proxy. So while it competes at some things nginx is commonly used for, its not a full competitor (you wouldn't replace nginx+php-fpm w/ HAProxy+php-fpm).

That said, if you're looking for a proxy/load balancer, HAProxy is most likely the absolute best you're going to find anywhere, ever...and the price is right ;)

There's a fork of nginx, called tengine, maintained by the people at Alibaba.

http://tengine.taobao.org/

Conveniently this would support the authors requirements of syslog feature.