For NGINX users, please use the following rules:
if (!-e $request_filename){rewrite ^/(.*)$ /index.php last;}
(Provided by @imsoff)
For lightTPD users, please use the following rules:
url.rewrite-if-not-file += ( "^/(.*)$" => "/index.php/$1" )
(Provided by kk198)

If your TWIP installation have a prefix of /twip/, then you should use

^/twip/(.*)$ /twip/index.php

instead of 

^/(.*)$. /index.php

Just a reminder, please specify the index-file to "index.php"

lighTPD:

index-file.names   = ( "index.php", "index.html",
                       "index.htm", "default.htm" )

nginx:

location / { # it can be /twip as well
  index index.php;
}
