#1

Here are a few of the commands I have discovered (excluding the hundreds of emotes)...

Social
/t - Sends a /tell to another player
/tell – Sends a /tell to another player (alternate form of /t)
/whisper – Sends a whisper to another player
/reply – Reply to a whisper
/r – Reply to a whisper (alternate form of /reply)
/who – Opens the Who window
/hewho – Unknown
/group – Invites target player to group
/invite – Invites player to group
/say – Switches outgoing chat to Say, only players in local vicinity can hear you
/yell – Yells in chat, displayed in red text. This can be heard in a large area. Cross-faction /yell is possible
/general – Speak in General chat, this can be heard throughout the entire planet/flashpoint/instance
/trade – Speak in Trade chat
/pvp – Speak in PvP chat
/1 – General Chat shortcut
/2 – PvP Chat shortcut
/3 – Trade Chat shortcut
/4 – User chat channel
/5 – User Chat channel
/6 – User Chat channel
/7 – User Chat channel
/8 – User Chat channel
/9 – User Chat channel
/0 – User Chat channel
/guild or /g – Chat only to your guild
/gsetrank – Sets player rank in guild
/gquit – Leave your current guild
/gabdicate – Gives guild leadership to another player (thank you CkVega!)
/gdisband – Disband your guild if you are leader
/promote – Promotes player in guild
/officer – Speak in officer only chat
/ginvite – Invites target player to guild
/gremove – Removes target player from guild
/duel – Request a duel from target player
/friend – Add a player to your friends list
/follow – Follow target player
/date – Displays Date information
/roc – Raid Officer chat
/flag – Flag yourself for PvP
/dnd – Flags you as Do Not Disturb. Useful when you want to be left alone in the galaxy
/emote – Allows the player to write his own custom emote (ie. "/emote punts the Ewok" would read "PlayerName punts the Ewok")
/invite - Invite player to group

Misc
/stuck – Helps dislodge a player from environment
/bug – Allows player to lodge a bug complaint/report
/logout – Logs player out of game and back to Character Select screen
/quit – Quits the game completely
/dismiss – Dismisses your companion
/nameplates – Shows player/npc nameplates
/inspect – Inspects another player
/selljunk – Commands your companion to go sell all your gray items

UI
/quickbars – Toggle additional quickbars in UI
/coverbar – Toggle the cover bar in UI
/me – Unknown
/setactionpointdisplay – Unknown
/subtitles – Displays subtitles during mission cutscenes and other scenes.
/hideui – Hides the User Interface, alternatively you can use Alt+X to hide your UI and Ctrl-U twice to reset your UI

#2

/gabdicate – Gives guild leadership to another player