GG. Should I bother?

When I message "GG" after a game no one responds. No offense. Just on to their next game I guess. Should I bother with the GG at all? 

It is good sportsmanship, but no big deal either way.

People might be taking it as an insult/sarcastic/condescending if you beat them or if they blundered a lot. If you're playing blitz or bullet, yeah they probably moved into the next game already. It's a gaming term which is often used in a cruel way, as well as a friendly way which complicates things, plus a lot of people aren't necessarily going to feel it's appropriate for chess.

You could always try sending a different message which communicates the same thing in a way which is clearly friendly, and possibly sending it shortly before the game ends. Such as "GG, you honestly played great" if you're about to win or "oof well played" if you're about to lose. Or some other specific compliment about an aspect of the game. I've made a lot of friends here that way, and people are much more likely to reply, if that's what you're looking for.

What I don't recommend is switching to saying just "GG" alone before the game ends- it'll be even more likely to be taken as insulting (or as stalling). And if they blundered a lot you should say something sincere or not say anything, nobody wants to be patronised that they played well when they clearly didn't. Just go with common sense.