I've got my mini hooked up in one room to a TV. It doesn't really have easy access to a keyboard and mouse, but it is connected to a huge external hard drive that I store all sorts of files on. So sometimes, when the mini is asleep I need at the files. Searching on Google for "wake mac on lan" took me to this older hint, which hasn't had much action lately.

After trying the hints on that page, the problem was that after waking the mini, I would still have a terminal window open. Now there may be away around that, but I couldn't find one. So I took the information I learned there and plugged it into an Automator workflow, using the Automator: Run Shell Script action. The Shell should be /usr/bin/python, the Pass input should be to stdin, and the body of the script should be:

#!/usr/bin/env python
import socket
s=socket.socket(socket.AF_INET, socket.SOCK_DGRAM)
s.setsockopt(socket.SOL_SOCKET, socket.SO_BROADCAST, 1)
s.sendto('xff'*6+'x00x11x22x33x44x5a'*16, ('192.168.1.255', 9))

You will have to replace the 00, 11, 22, 33, 44, 5a with your own mac address, of course -- you can find this in the Network System Preferences panel.

Then save the Automator action as an application or a Finder plug-in. When it is run, there is no Terminal window. (I saved mine as an application, changed the icon to a picture of a mini, and now I have an icon in my dock that, when clicked, wakes my mini in the other room).