This might fix your problem, as it did for me (AIM accounts):
Messages / Preferences
1. Account informations :
- uncheck "enable this account"
- make sure the user name does not have "@xxx.com" at the end.
- make sure your password is there
2. Server settings :
You probably have : api.oscar.aol.com
Port : 443, SSL checked.
----> Uncheck SSL
The server changes itself in : login.oscar.aol.com, port 5190.
3. Account informations : enable this account.
You probably will asked to enter your password, and it will return that it is wrong. Don't worry.
Quit Messages, wait 10mn or so, then open Messages and it should connect automatically.
If it says "Offline", click "available" to connect.
In Preferences, check your password is there, if not, enter it.
Now you should be able to use audio, video, and screen sharing as well.
You can also use : login.oscar.aol.com, port 443, SSL unchecked.
This fix worked for me on Mountain Lion and Mavericks.