Maybe the conversation wasn't particularly exciting for the other party. Or perhaps they just didn't want to talk to me. A verbal indication that the conversation has come to the end, coupled with a final salutation, should be not only common sense, but also good manners (or netiquette). Don't just leave me hanging! When I go back to check my Facebook tab and see that the reason my chat partner hasn't responded in a while is because they randomly signed off, I'm left feeling a bit like someone hung up on me.
I know, this probably isn't a big deal and I'm sure most people would say "who cares?" But manners matter, pure and simple. I always try to make an effort to say goodbye to people in a chat conversation because it just seems like the decent thing to do. I would never hang up on someone without saying goodbye (unless the point was to hang up on them, as if to make a point) and generally speaking when it's done to me I become quite perplexed. Just because we are sitting at computers does not mean we should abandon our manners.
And with that, goodbye.