It's lucky we're doing structure right after genre, because the two have a lot in common. A romance runs very specifically, so that when you read or watch one you know it's a romance. A heist, on the other hand, is almost completely different. Yet, both of them have the same fundamentals (main character wants blank, and must do blank to get it). What's the difference? Merely the structure of the story.
Learn the overall structure of a story through the act systems, then get more specific with the genre you want to write. I'll go over a couple of the most obvious genre structures here. And remember: although some genres have inherent structures, you don't have to follow any of them to write that kind of story. Sometimes it's just easier.
I like heists, or capers as they're sometimes called. Why are they so intriguing? The main characters are so good at their jobs, it shouldn't be legal. (Ahem. I mean in terms of storytelling.) How do you make a story work when your main character is basically, well, me?
Being writers, I think we all know. Heists rest on this single problem: when you make a plan, it doesn't always work. When I plot a novel, I get about halfway through before I realize the wrong people are kissing, the villain loves kittens, and the best friend is probably an alien. When I discovery write a novel, I often find out the same things, but it doesn't bother me because I expect weird things to happen. When you have a plan and the smallest thing goes wrong, DISASTER.
That's the basis of a heist. Everything goes wonderfully until about halfway through, where something goes wrong. Everything starts to go downhill until the team pulls victory out of a hat. All heists are different, of course, but the big reason heists have their own structure is this: the characters are amazing at what they do until about halfway through, when everything begins to tumble down around them. In any other story, the villain is supposed to be the amazing person, and it's generally not wise to have the main character winning before his time. In heists, however, it works.
One of my other favorite structured genres is the thriller. Many look at the thriller as just a mystery where the murderer is still loose, and that's okay-- but I binge-watched Fringe after my time as an icicle. Five seasons of supernatural one-hour thrillers teaches you a little something about a structure that works. No, not all thrillers do it this way, but this structure is consistently successful. It happens in a series of deaths.
Death 1: a person we just met and only slightly care about dies. They probably have kids, or a puppy, or something, but they must die for the sake of story. This is the same as in any other crime show: first thirty seconds, you get a murder. Enjoy. The team of detectives begins to investigate, but can't really find anything conclusive.
Death 2: right around halfway through the story, another person dies. This death is like the first-- we only know a little about the victim-- but the detectives find a vital clue at the crime scene. They begin to understand something about the killer, such as his modus operandi or preferred target. They make some headway in the case and finally realize where the person is going to strike next.
Death 3: not exactly a death, just an attempted one. In the course of their investigation, the detectives realize that the murderer is going after someone we know. Perhaps it's a friend of the first victim, but they're really pleasant and unworthy of death-- perhaps it's one of the detectives, or a relative thereof. Someone important is in danger. The detectives realize this, rush to the location of that person, and catch the killer.
This format is so powerful because it puts someone we care about in danger. It isn't simply three people dying, nor is it a killer hunting after a single quarry constantly. It starts out very clinical and matter-of-fact, then steadily gets more and more emotional until the suspense is screaming. It's gripping from the beginning, but that increasing suspense really packs a punch.
I consider heists and thrillers to have the two most distinctive structural differences in genres. In a romance, you can structure it blow-for-blow along the Hollywood Formula, or even the Hero's Journey. The same goes (obviously) for a quest; the same goes for a post-apocalyptic paranormal romance horror novella. The thing about heists and thrillers is this: you can have an epic fantasy heist, or you can have a science fiction thriller. These are less genres than they are structures, and they can be translated into other genres very easily.
Are there other such structure-genres? Of course there are. Sports stories (key feature: the montage), romantic comedies (key feature: bad decisions and schemes), or armchair mysteries (key feature: Miss Marple). All of these have inherent structures, but none of them are quite as pronounced as those of heists and thrillers.
Remember this: although some genres have structures stapled to them, you don't have to follow them. Write your science fiction heist. Write a romantic comedy thriller. This goes back to the genre-bending post Stark had last month, but it also works for structure. Not every bullet point of every structure must be followed. You are your own writer.
So write, and have fun with these. They have good track records-- you can't fail.