I did something like this a couple of years ago. It was (I like think) fairly secure and only accessible to a limited number of pre-vetted, authenticated users, but it still left me with an uneasy feeling! If you can avoid doing it, I'd recommend you do :)
I had a database sitting between the frontend web-tier and the script which was actually executing actions. The relevant table contained a symbolic command name and an optional numeric argument, which was sufficient for my needs. This allows you to audit what's been executed, provides a quick and dirty way to have a non-www user do things, and means if the website is compromised they're constrained by the DB structure (somewhat) and the script which pulls data from it.
The data from the DB can be read by a daemon running in a separate, unprivileged account. The daemon pulls and sanitises data from the DB and maps the 'command' to an actual executable (with a hard-coded map, so commandA executes A, commandB executes foo, and anything else would get flagged as an error). The account can be locked down using AppArmor (or SELinux, I imagine) to prevent it from executing, reading or writing anything you don't expect it to. Have a system in place to alert you of any errors from either the daemon or AppArmor/SELinux.
The executables which the daemon runs can be setuid'd if appropriate, or you can use the sudoers
mechanism to allow the unprivileged account to execute them without a password.