Why use Apache over NGINX/Cherokee/Lighttpd?
Apache's .htaccess provides flexible configuration. This allows users on a shared host to customize certain settings of an apache without having to alter the core apache configs.
It is the standard server bundled in typical LAMP setups, although, many services use other web servers for in conjunction (like static files, video streaming, etc.).
Since Apache is popular, it's easy to find a solution to any problems.
Other than that, other solutions would probably be better.
Apache IS asynchronous if you want it to be with the Event MPM. Unlike Nginx and Cherokee, etc., it is not the default.
Apache's made some important moves in 2.4 so it can be more competitive — esp. as it pertains to serving static requests using the Event MPM. Various benchmarks don't speak well of this, but:
It's very difficult to ascertain how much slower Apache is in 2.4 because Apache's out of the 'box' configuration is detrimental to performance and legacy holds it back in some respects. For example, .htaccess requires stat/reading a multitude of files on every request, which may include many rules and regexes. Nginx doesn't have this problem, nor does Cherokee. Litespeed has .htaccess support in Apache's style, but only if you pay for it. Most benchmarks don't turn off features like those.
Most of the benchmarks are also ridiculous in that they're run locally and over a GbE network or similar. A real web server has to cope well with various speeds, including 3G phones. It could be that Apache's performance is better in the real world.
I doubt it.
Nginx is still faster, and I might choose it, but Apache isn't asleep.