All of these chat commands can be used in any chat channel. For SC and WC2BNE users, they can be used during game setup or while a game is in progress.

*Note: All of the following text was taken directly from the Blizzard webpage; I wanted to include as much information as possible, and they do a good job of it themselves. :)

/whois [user] - (Ex: /whois TPark or /whois #133115)
Looks up some basic information on a user, including their account number and their current location. This is an excellent way to find your friends online. typing /whois #[number] (E.G. /whois #1).
Aliases for this command: /where /whereis

/whoami - (Ex: /whoami)
Displays your information on Battle.net.

/whisper [user] - (Ex: /whisper JohnS or /whisper #236325)
Sends a private message to a user online regardless of the channel they are in. This is an excellent way to let a friend know you are online.
Aliases for this command: /w /msg

/squelch [user] - (Ex: /squelch BFitch or /squelch #223251)
Ignores any future messages from that user effectively muting that user to you.
Aliases for this command: /ignore

/unsquelch [user] - (Ex: /unsquelch BFitch or /unsquelch #223251)
Allows a previously squelched user to talk to you normally.
Aliases for this command: /unignore

/away [text] - (Ex: /away eating dinner)
Displays a message that you are away from your keyboard whenever someone whispers to you or does a /whois command on you. To disable this command, use the command again.

/dnd [text] - (Ex: /dnd sorry playing a game with GFraizer)
"Do Not Disturb" - prevents ALL whispers from displaying to your screen. Its use is similar to the /away command. To turn the DND mode off, just type /dnd without a reason. This will prevent people from sending whispers to you while in a game as well. You are still able to see all normal public channel messages.

/who [channel] - (Ex: /who Open Tech Support)
Displays a list of all users in the given channel.

/stats [user] ID - (Ex: /stats DavidN STAR or /stats #42 STAR)
Displays the player's Win/Loss/Disconnect record for both normal and Ladder games.
    STAR - Starcraft
    SEXP - Starcraft Expansion (Brood War)
    W2BNE - Warcraft II Battle.net Edition

/users
Displays the number of users currently on Battle.net.

/time
Displays the current Battle.net time.

/channel [channel name] - (Ex: /channel Blizzard Tech Support)
Switches to a channel without having to use the channel join screen.
Aliases for this command: /join

/me [text] - (Ex: /me is rolling on the floor laughing!)
Displays emotion text, as in "PatN is rolling on the floor laughing!" This command currently works only in Starcraft.

/designate [user] - (Ex: /designate AlenL or /designate #423262)
Selects [user] as the next channel operator when you step down, either by resigning or by leaving the channel. If the channel Operator leaves the channel and has designated more than one person, the last person designated will have ops.

/resign
Step down as channel operator and become a normal user again.

/rejoin - (Ex: /rejoin)
Makes you rejoin the channel you are currently in.

/kick [user] - (Ex: /kick TwainM or /kick #234226)
Kicks a user out of the channel. This is best used as a warning since a kicked user can return at their leisure.

/ban [user] - (Ex: /ban RobertB or /ban #137389)
Kicks a user out of the channel and prevents them from returning until the current operator steps down or leaves the channel. This is the most powerful command at an operator's disposal, use it wisely.

/unban [users] - (Ex: /unban RobertB or /unban #137389)
Allows a banned user to return to the channel.