Have a look at
lighttpd and the already mentioned nginx (I personally prefer the latter for my projects. I think it is more stable and has got a cleaner code base. However I never tested DokuWiki on it). Like Apache, nginx and lighttpd provide a large community and therefore much more community support than other projects.
For sure, there are even smaller (but less feature complete) webservers with FastCGI support out there (FastCGI enables you to connect your webserver with PHP if there are no recommended solutions like mod_php for Apache), e.g.
gatling. But because most of these do have a really small user base, you'll probably have to solve all problems by yourself (and probably nobody in here can say if DokuWiki runs without problems, you have to try it out ;-)).