How serious is your d&d?

In-game - Ranging from semi-serious to very serious.

At the table - not very serious at all.

Depends on the kind of gaming I'm running. Last campaign was fairly dark and epic, based on demonic themes and keeping them at bay. Current campaign is much lighter, being a series of various only semi-connected adventures, but some of them have darker themes. In either case, the sessions themselves sometimes devolve into hilarity, due to inside jokes and such.

Campaign is mostly serious but lots of fun and funny moments from the players.

I would say on a scale of 1-10, the campaign has a seriousness level of about 9. Around the table, the players have a seriousness level of about 5 at best. I attribute that fact to a group of guys who have played since early college, which was ~35 years ago, and so when we manage to get together to play, a lot of humor and old experiences rise up and overtake our playing. But no one seems to mind. That is just how we play due to the amount of time in between we actually see and are able to talk with each other.

I'm serious enough as a DM that I spend 8 - 12 hours simply preparing for a 4 - 6 hour game session. I want the PCs to have as good a time in the session as I possibly can make it so try to do all I can in that regard. It's mostly still not perfect but I typically come away from any given session having learned something that will help a future session.

As a player I'm serious enough that I will do my best to hone my role-playing as it fits with the character I have created as well as the campaign itself. This is something I have only really embraced in the last few years since I have come back to the game. When I played previously I was fine with hacking and slashing my way through dungeons with nary a spoken word by my character.

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I tend to keep things fairly light-hearted - swashbuckly would be the adjective I'd use.I don't want to go super-deep and dark (despite that, undead are some of my favorite monsters), but I don't want to have to deal with constant zaniness "for the lulz." And of course, a lot depends on the players at the table, and their approach.

In a nutshell, just serious enough that I can maintain the illusion to myself that, should I ever write out one of my campaigns as a novel, movie, or TV show, it would be worth watching as a drama/action/not-comedy.

In other words, the story line is reasonably serious, with tension-breaking humor and the like totally acceptable. But... we're all friends (I've known a couple of the players for close to 30 years) and we're together to have fun. So, it probably plays more like seasons 6+ of Supernatural, where you know the cast and crew is there just because they're having a good time, Scooby Doo episodes and all. But, I hope you can still see the conceptual foundation that was present in seasons 1-5.

The only explicit rules I have are:
* No joke names. They're just too hard to shove behind a curtain when we do want a serious scene. Like having one actor in Die Hard who thinks he's doing Airplane.

* No gender bending. I don't have any theoretic issue with this. I've just exhausted my limit of bad experiences and have no interest in putting my hand on the stove, again. I'd probably bend or even toss this one, at this point. But, it came about when I was younger and had a looser membership in my group. I was always shocked at which guys were latent misogynists with a leather fetish -- something I really didn't want to know.

* No Wuxia or similar tropes. For most genres, I have a cap on my ability to suspend disbelief for "mortals". 1980s action movie physics is fine. Having some mages around is fine. Having Conan do a flying, head-first, horizontal spin across a 15 foot gap while exchanging sword play with the BBEG, not so much. Steampunk devices generally fall into this one, too, as they're too improbable. If we're playing a supers game or something similarly high-powered or magical (Sons of Ether, for example), it's a different story, but those aren't about "mortals".

I tend to design campaigns that are somewhat serious, but my players are all friends and very silly so it often descends into the goofy very quickly. In a recent session of HotDQ the party band did an "Enthralling Performance" dance (which she pantomimed irl; this was even timed) while Cyanwrath was trying to goad one of the PC's into another one-on-one duel. Both berserkers failed their save, and by the time Cyanwrath gave up on the PC he noticed they were charmed and just left. I'm waiting for a good moment for him to pop back up again.

Similarly to many posters above...

The themes of our games are pretty serious. Not too grim dark, but no forced humour from the scenario or "it would be funny if..." situations. The players are well able to bring it up on their own.

The characters are seriously "made"; they may have their quirks, but no attempts to be deliberately cartoony, ridiculous, or blatantly inefficient. Gender-bending or racial/cultural experimentation are cool as long as no disrespectful stereotypes are used; respect too is taken seriously. No "pun" names either.

The players play their characters seriously in the sense that they all have their characters to heart and see to their survival and growth, knowing that even the greatest heroes can have their flaws, or sense of humour for that matter.

The characters themselves take their quests/tasks/duties seriously. Too much I warrant.

We all take our hobby seriously, knowing that the main goal is to have fun, and that fun involves a good part of humour. There is plenty of laughter and jokes all around.

TL;DR: Our time together is precious; more than our time playing our characters. We do not take our hobby lightly, which means being serious about allowing humour to seep in.