We use Litesepeed and love it. Many have suggested that we witch to nginx or lighttpd to save money, but the problem with both is that they are not compatible with the vast majority of sites. .htaccess is just one example.
Litespeed is a drop in replacement meaning that the panel doesn't even know it's not seeing apache. It works great, increases performance, is more secure, but does cost money.
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If you're looking to setup some load balancing (which I don't think you are), then nginx is probably what you want. In it's easiest form, I've seen it used to serve all the static content (images, etc) - especially on image heavy sites. You can also use it as a load balancer by proxy, or as your web server by running php_fpm.
I think what you're looking for though is just a very streamlined and fast webserver that you can use to replace Apache with. In that case I have to mimic what Scott said, and advise you to check out Litespeed. Many providers now offer discounted License's too, so the cost is slowly becoming less of a problem.