I had created a post here regarding a Varnish plugin we wrote for cPanel over a weekend codeathon (http://www.unixy.net/varnish). Based on benchmarks, Varnish+Apache came out ahead of Litespeed. But benchmarks are not always conclusive since user traffic patterns are difficult to reproduce in a benchmark environments.
The feedback we've gotten so far on the plugin is very positive (google if interested). Nginx can do caching but not with the same flexibility as Varnish.
Varnish is good for caching any object; static or dynamic. The plugin we wrote uses Varnish to do a lot of dynamic page caching. Varnish is better at dynamic page caching than Nginx.
Litespeed has a caching mechanism too (introduced recently). But I think it requires an enterprise licesense of 2+ CPU. Here are some benchmarks of Apache+Varnish vs Litespeed: http://unixy.net/apache-vs-litespeed
For those that need hassle-free backwards htaccess compatibility, try litespeed.
But there a few nice alternative to apache these days.