Headless MacMini

If you have another Mac (10.5 or above) or an iPad or iPhone, you can remote into the Mini and control it as if you were sitting in front of it. There are two steps to get this working. The first step is to configure the Mini to allow screen sharing. Here are instructions if your Mini runs 10.6 (Snow Leopard):

Mac OS X 10.6 Help: Sharing your screen with other computer users

Instructions are similar if your Mini runs 10.7 (Lion):

OS X Lion: Share your screen with other computer users

The second step is controlling the Mini from another Mac:

Mac OS X 10.6 Help: Sharing the screen of another computer

OS X Lion: Share the screen of another computer

If you don't have another Mac, iPad or iPhone (heaven forbid), but you have a Windows computer, you can use VNC software. You still need to configure screen sharing on the Mini (first step above). Then, you need to get the VNC software on your Windows computer and configure it. Here are some good options:

http://www.wyse.com/products/software/mobility/PocketCloud
http://www.tightvnc.com
http://www.realvnc.com

I hope this helps!

This might be the simplest solution for shut down, but it requires a keyboard. If you press these four keys at the same time (Control-Option-Command-Eject), it will quit all apps and shut down the computer without any more interaction on your part. If you have any unsaved files open (unlikely if you're only using this as a music server), it will give you a chance to save changes.

I do control my mac mini with either an ipod touch or iphone and will try the screen sharing recommendation.
When I first got the mac I tried the VNC route but never got it to work as I'm not the most computer savvy guy. Maybe I'll get my 14-year-old grandson to set it up. ;)

I set mine to automatically shut down at 12:00AM and boot up at 3:00PM everyday. If I want to shut it down earlier, I use a VNC client from my iPad or iPhone to remote control it.

The auto shut down and boot up time can be set in:

System Preferences->Energy Saver->Schedule.

What I do is use some sort of VNC remote viewer software on another computer or an iPad (I use the free Mocha VNC Lite). Or, if you have another Mac use the built-in remote desktop. These solutions require remote access to be enabled on your Mac Mini. Then, just use the Shutdown menu item underneath the Apple menu. A keyboard or mouse isn't necessary for this.