I tried a few and settled with Bit Web Server. I also tried KSWEB.
Bit WebServer also comes with PHPMyAdmin (PMA) installed and you are ready to go.
You can install Drupal and Wordpress as well. I got Code Igniter running without any problems.
A few notes. These apps tend to be a bit buggy. They can force-quit or hang under load. I can't really blame them as the fault may be with Android OS itself or the hardware I am running. I've tried them with the Galaxy Nexus and a Samsung Galaxy Tab 2. I've been reading that the OS (Jelly Bean and ICS) may starve the apps due to power savings and other reasons such as auto close.
I can't really complain though. I'm not running anything mission critical. If the app crashes, I simply restart it. It comes in handy show off web apps.
Moreover, it runs LIGHTTPD instead of Apache so PHP run as a CGI.
The apps range from 2ドル to 3ドル. Yeah, you're paying for open source software and may have an issue with it. However, think about the time you are saving without having to resort to building PHP/MySQL from scratch and make it work on your phone. I have no problem with the pricing.
Just add a keyboard and you are ready to go!
Links:
Bit Web Server
KSWEB.