Open your Applications/Utilities folder an launch KeyChain Access.
With the Login item selected top left and Passwords lower Left look up the ID/Screen Name on the panel on the right
When you find it double click it it bring up the Info panel
Tick the Show Password box
(It will bring up a dialogue box asking for Your Mac User Password and then click Allow Once)
The lower Text field of the Info panel should now show you the password.
The above will work if you entered the password in iChat and asked it to be saved.
If you choose not to enter it in iChat so it was stored then you will have to got to the web site where you registered the name.
iForgot can be used for Apple IDs ending in @mac.com or @me.com
For AIM registered name start here Use the Sign In option top right then the "Forgot Password" option at the Login in page.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.4)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.7.4),
"Limit the Logs to the Bits above Binary Images." No, Seriously