It would be useful to know the iChat version and the type of Account (Screen Name or ID) you are using.
For Instance an @mac.com name will work as a AIM valid Screen Name.
Depending on which iChat version you will determine which items are in the Add Account drop down (with ichat 6 there is only AIM and you have to enter the name in full).
@me.com and @icloud.com ending Apple IDs are also valid Names but you have to using iChat 6 (or Messages in Mountain Lion) to Login due to extra security Apple uses on those IDs.
They will not work in iChat 5 or earlier.
If you have changed the password at Apple recently and gone over their 16 character limit AIM has you also will not be able to Login.
If you have an AIM name or an @mac.com name then try signing in here.
This may tell you if your account has been suspended.
Staying with AIM there can be issues with an SSL login sometimes.
Manually change the "Enable this Account" and then tick the box again.
If you were suddenly dropped by the server the .plist involved may have a different state to what the server thinks (it says you're Logged in when the server says your not) At this point it will tend to think you are not you and refuse the login.
There can be similar issues with Jabber (Google) logins.
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.4)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously