I often do branch prediction when chatting on IM's, especially with people who type slowly. For example, I ask "How did your exam went?", and before getting the answer, I type (without sending) "Sorry to hear that, but hey, you'll have another chance next week." In general, I just quickly think about possible answers, select the most probable one and type in my response without waiting. Then I get answer from the other person, and most likely send my text immediately.

Most of the time, branch prediction works great and it's a big chat optimization. If it fails, it is often of because the other person answered in a way, that my prepared sentence won't fit grammatically (I just edit it), or asked for clarification (I then CTRL+X my response for later reuse and write some clarification instead).

I think I've realized it when I started to extensively use Skype chat, which (as opposed to - for example - IRC) shows that a person is typing. When I'm asked a question and then I see that the other person is typing something, I wait with my answer, expecting a clarification or follow-up statement from the person I talk to. I guess others do that too, so I consciously avoid branch-prediction typing on Skype in order to actually get any answer from the other person.