usually, a gg will suffice.
Checkmate etiquette

I think as long as you stay away from things like "How do ya like me now sucka!" or "I own you!" you won't offend.
Of course, you'll quickly find that while chess is filled with wonderful people, there is a subset of whiney little (insert banned word) too.
Just include something like "gg" (good game) or something similar and you're fine. There are always going to be poor losers that just try to cause controversy but don't worry about them. As long as you are polite and respectful, you'll be fine.

I think it depends on if you have been chatting with the person at all during the game. If my opponent and I have been talking friendly throughout the game, I will certainly say something at the end of the game (win or lose), e.g. "good game, let's play again sometime" or something like that. Or if you and your opponent seem to "play nicely" for lack of a better expression, you could ask them if they want a rematch.
On the other hand, if we haven't been chatting at all during the game I usually don't say anything, maybe "good game"
Do people get irritated if they are checkmated with no chat at all? Would you always hope for at least a gg, or somesuch?

I am new to Chess.com, and would like to know, before one of my opening games gets too close to its conclusion, whether it is considered normal, good form, or poor form, to send a message with your checkmate move - a 'thanks for the game' or somesuch. What normally happens? Of course I may never win a game, which would save me from the decision, but I wouldn't like to offend.
I'm surprised that no one has mentioned the "Trophy" feature of this site. In addition to sending a "good game" chat message, I encourage you to send your partner/opponent a Trophy. As you'll see, there are many, many Trophy "templates" that you can use; some simply say "Good Game," while others focus on a particular strength that the person demonstrated during the game (e.g., "Connoisseur of the Queen"). Some are tongue-in-cheek. To my knowledge, the Trophy feature is unique to chess.com, and it's part of what gives this place a positive feeling of community. Give and receive lots of Trophies -- it's fun!
I never talk about a checkmate move ahead of time. I sometimes use conditional moves. I usually thank an opponent after the game. Sometimes I send a trophy. When I have a overwhelming position and pieces, I sometimes use the phrase "Turn Out The Lights The Party Is Over." A phrase Don Meredith used when a professional football team had a huge margin of points and time was running out with almost no chance of recovery. Actually Don would begin to sing this.

I agree with the previous post. Conditional moves in a winning position indicate that you are confident that the game is trivial and even if your opponent was hoping to either run your "correspondence" clock or just antagonize you, he's only just talking to the "hand/server" and not you.
Saying "gg , thx" before (as opposed to "with" the final) checkmate is a little disrespectful of your opponent's right to choose to either stay or resign. We've all been in his shoes before and nudging somebody to walk is downright rude.

All good comments here. I like to chat during a game, but many do not. I can usually feel this out pretty quickly. I almost always offer a "GG" or "Well Played", etc at the end. I always start out with "Best of luck to ya". Not sure why I do that bit though.
As previously mentioned, it's a personal judgement in most cases. I would never comment on the outcome of a game before it's concluded, unless it was against a friend and I knew they wouldn't mind.
NEVER brag! The Chess god's will humble you by forcing you to blunder away your queen and the game to an opponent rated 300 points below you if you do... or worse. :)
I am new to Chess.com, and would like to know, before one of my opening games gets too close to its conclusion, whether it is considered normal, good form, or poor form, to send a message with your checkmate move - a 'thanks for the game' or somesuch. What normally happens? Of course I may never win a game, which would save me from the decision, but I wouldn't like to offend.