Most popular Internet Messengers avail an option to go invisible, but GTalk doesn’t ! But here are few ways you too can go invisible on GTalk :
1> Login to Gtalk from within your mail and not desktop client. Here you have an option to go invisible. But you should be aware of the fact that even if you logging to your desktop client simultaneous, when you are invisible in Gmail, you loose that status and whatever status the desktop has will override and hence you’ll be either busy / available / idle.
2> Download and install GTalk labs edition ! Yes, for those who din know there is a labsedition, and get it go to Google Labsedition download and install it. The labs edition GTalk has an option, that lets you go invisible. There are other advantages with the labs edition, like : group chat, Desktop notification from Gmail, Google calender, Orkut and more !