I've recently deployed a couple of apps using lighttpd. It works well, and I have had nothing but problems trying to use apache.
I've looked at mongrel and litespeed as well. Mongrel seems to work well, and I'd like to use it because it would take advantage of our hardware load balancer, but lighttpd offers easy, powerful configuration, and it's really fast. I haven't used sendfile, but everything with lighttpd seems to be easy to use and works well. I'm strangely attracted to Litespeed, but the free version doesn't offer sendfile support.