Bind a key, and copy text from whatever your mouse is hovering over.

Chatframes, QuestText, Menus whatever.

You can bind a key from the blizzard key bindings configuration menu.

The following slash commands are supported:

/cpyt <Name of Frame>

This is mostly used for the chatframes, eg.

/cpyt ChatFrame1

you can bind keys to copy the frame that your mouse pointer is over, or the game tooltip (since you cant mouse over it).

I suppose you could also use: /cpyt GameToolTip