There are a LOT of commands and variable you can play with in Quake III. These only begin to scratch the surface, but are some of the more useful and interesting ones. Keep in mind that some of these can only be used while in "cheat" mode, and other settings may be locked on certain servers, in the interest of keeping al players equal.
If you want to see the complete lists:
/cmdlist - will produce a list of commands
/cvarlist - will produce a list of console variables
You can also output this to a text file by typing

/condump filename.txt
This will output the contents of the console to a text file in the Quake3/baseq3 directory.

/reconnect
Will reconnect you to the last server you were connected to. Useful if Q3 dumps you to the main menu during a map change for no apparent reason.

/bindlist
Will produce a list of all currently bound commands.

/bind
One of the most basic commands, this will "bind", or assign a command to a particular key.
Usage: /bind " "
Example: /bind space "+zoom"

/say
Will produce a chat message onscreen. Used with the /bind command, this is an easy way to set up chat messages.
Example: bind F5 say "ouch! that hurt!"
Do NOT abuse this command. Spamming servers with lots of useless chat is an easy way to get kicked off a server.

/say_team
Allows you to send private messages to your teammates. VERY useful for Capture the Flag matches.
Example: bind I say_team "Defense: Incoming Enemy!"

/messagemode 2
Bind this command to a key to enter "team chat" mode. Anything you type after this command will only be sent to your teammates.

/kill
Will cause you to commit suicide. A handy way to lose a frag.

/callvote [proposed vote]
This command can be used to propose changes on a server, and allow all the players on the server to vote on it. This can be used to change maps, game modes, settings, and even kick players if necessary. To vote on a proposed change, press F1 to vote "yes" and F2 to vote "no".

Examples:
callvote map q3dm9
callvote g_gravity
100 callvote kick sluggo

/quit
Quits the game.