I love writing the dialogue, and I love reading it. Give me a good conversation any day. Action scenes are fun, too, but when characters start talking and interacting in believable ways, you hook me. Especially if I can see what the characters really mean, if I can get a sense of the undercurrents of their thoughts and all the things they're not saying. A good conversation moves everything forward. It tells the reader about the world, about the characters, about the conflict, about the plot.
The way characters talk to each other says so much. Their choice of words, the non-verbal cues, the tone of their voice and the way they act around one another. And how that changes when a third or fourth person is added. The subtle dynamics between people rendered in ink and spelled out if you read between the lines are not easy to accomplish. I sometimes spend days on certain conversations and then go back to them over and over, and just never seem to get them "right."
For any scene with multiple people in a dialogue, I make sure I know which characters are present, so that each of them is represented in the scene and no one turns invisible halfway through. Obviously, if there are a lot of people, some are going to be doing more than others, and some might get grouped together for ease of reading, but when there's only three or four, sometimes one can stop talking and reacting and just sort of slip away into the background.
Not everyone has to talk, of course, some characters prefer to sit in the background and make faces, or just listen, but I think it's important to note this for the reader. Otherwise the character becomes invisible.
I think it's also important to try and create a sense of which characters are having discussions of their own. For instance, if there are four characters in a scene and characters A and B know something that characters C and D don't, A and B might be exchanging looks at relevant points. Of course, if they don't intend to tell C and D, maybe they're pointedly not exchanging looks.
While body language helps when there are only two characters talking, I think that as a conversation gets more complex body language becomes a larger part. If a character is addressing a large audience, you can't give the reactions of every audience member, but you can give the reactions of groups within the audience. For example:
"Avery's supporters cheered in response to his announcement, but some among his opponents booed and others shifted in place, casting narrowed-eyed glances at one another."
That tells the reader a lot and hints that some of his opponents may be forming a plant of action in regards to Avery's announcement. Here, the body language conveys a reaction that isn't possible in words. No one wants to shout out their conspiracy plans, after all.
I think another good example of body language is when someone is eavesdropping, in which case the body language they observe becomes a big part of the conversation. They draw conclusions--and maybe not always the right ones--from how people are sitting, how they interact with whoever they're talking to, whether they look nervous, etc.
And, of course, no conversation would be complete without actual dialogue! I'm very much still working on slang and nuance when it comes to the language that people use, because it's such a big territory. From phrases used only by certain characters (whether it's because of where they grew up, or their religion, politics, class, etc.) to the way subcultures within a given culture speak to one another as opposed to how they speak to "outsiders." Even if you don't plan on creating your own language (and created languages are huge for some writers) there's just so much to consider.
I think that those little touches can really make a character, setting and conversation come alive, but of course they have to be used in a way that isn't a stumbling block for the reader. That balance is a difficult one to strike, but worth it when it happens.
A conversation should also move things forward, whether because the characters are learning new things, or because they're coming closer to some decision, or because the thing they've been hiding has finally come out. Those kinds of conversations are the ones that I like the most.