Teaser trailers are typically made far in advance of the film or game's release; their job is to embed their imagery into people's minds and stay in there despite not providing much context or story. This is why the images, shots or visual effects in teasers are some of the most spectacular and/or striking; every shot needs to pull its own weight.
The mantra of the teaser is to do more with less. This is both a smart and practical choice. Early in production of either a film or game (especially a game) there's very little to work with that is finished enough to show anyone. Early in production, big budget blockbuster films have very few if any finished visual effects, and most games look incredibly broken until the last few months of development.
The tricky part to creating a good teaser is to hone in on the most potent parts available, whether it's the: visuals, ideas, premise, mood or iconography. Which approach you taken depends entirely on what there is to work with. Well known franchises can often provoke strong reactions with little more than a logo. A common tactic in teaser editing is to obfuscate the reveal for as long as possible by avoiding shots with the franchise's iconic imagery until the very end. The teaser for Batman Begins operated on this structure.
This approach is effective because a logo reveal can be a nice surprise (provided the audience have any interest in the franchise). On the flip side, knowing that the teaser is for Batman can be fun because seeing a lot of not-obviously-Batman footage can feel like seeing the story through new eyes. The teaser for The Dark Knight is even more minimalist. By the time the Batman logo is revealed, they pile on a second reveal that this story features The Joker.
The teaser for The Last of Us Part II is another great example of a teaser that starts in ambiguous shots that are then re-contextualized by a logo. I first saw it at the PlayStation Experience event in Anaheim where the teaser started playing with no preamble. The forest shots didn't scream any specific franchise, but when they revealed the logo of The Fireflies, everyone knew it was a sequel for The Last of Us.
The recent teaser for Venom tried to take this approach, but the problem is there's only one shot that ties it to Venom's story, the black goo in one shot. The reveal was supposed to be a "WHOAAAAAAAAA" moment, but because virtually nothing in the teaser actually teases or entices the audience, it ends up being more of an "Ohhhhkay????"
Another teaser editing approach is to cut together a very wide view of the story, but provide very little depth. The teaser for the first Avengers film uses this approach. The teaser re-introduces the characters, the premise of bringing the superheroes together, and some vaguely threatening words from Loki. As with many teasers, there are shots with incomplete or missing visual effects. The shots of the cars blowing up are missing the energy bolts and aliens flying around causing the explosions, but cars exploding still looks cool, so it makes it feel kind of mysterious, because you want to know what's blowing them up.
The teaser for the first X-Men film is a great example of a terrible teaser. There are virtually no visual effects, and then they show far too many of those unfinished shots. There's a shot of Cyclops touching the side of his visor which clearly should've had him shooting his eye beams (and in later trailers does), but the visual effect isn't there so you just see some flashing red lights. Seeing a lot of unfinished shots from what we can assume with be a VFX heavy film is just not a good look. A better approach might've been to take just a handful of shots from the film that read like "THIS IS X-MEN" and set it to some better music. Less is more is another effective teaser editing style.
The Star Wars films used this short teaser approach to great effect, for example Episode II's teaser which was a series of shots set to the sound of Darth Vader breathing, and some light music score. The first teaser for The Force Awakens' also used this approach. If you look at those teasers, especially for The Force Awakens, each of those shots could easily be a still image used for a press release about the film. The editing and music help a lot, but the visuals stand comfortable on their own.
The teaser for Independence Day is another fantastic example of using very little footage, but cutting the teaser around just one idea. The slowly creeping shadows leads us to the logical next question: "What is so big that it's causing such an imposing shadow?" The visual effect of the White House being blown up seals the deal, you HAVE to know what comes next.
The other even MORE minimal approach is to just take a few scenes to make up the teaser. These teasers are often very similar to trailer cold opens. The teaser for Cloverfield is one such example. There are some party scenes, a rooftop scene, and then the rush to the scene on the street where the Statue of Liberty's head lands. Gravity also has trailers that were very minimalist in this way. While still a mix of scenes, they played as one. These teasers work on the strength of their premise which is quickly established in each one.
Lastly, the most famous teasers tend to be comprised entirely of footage that aren't in the finished film. Many disaster films in particular had very good teasers such as the 1998 film Godzilla teasers which start off by setting a scene, and then Godzilla somehow reveals himself. Godzilla's foot crushing a Tyrannosaur's skeleton is not something that is easy to forget. The teaser for Terminator 2 depicts the Terminator factory is another famous teaser that is a personal favorite, and nicely fleshes out the world.
Some CG animated films often have teasers that don't show any footage from the game or film, but are still representative of them. Pixar frequently makes teasers like this such as the ones for Monsters Inc. and The Incredibles. These serve as short films that give the audience a little flavor of each story.
Similarly, a lot of big budget video games are announced with lavishly produced CG short films like for Assassin's Creed Revelations, Dishonored 2, Mass Effect 3 and many more. Having these shorts produced by 3rd parties free up the developers to work on the game which may take many years to look presentable to the public.
In short, image is more important than story. If you start with story too early in the marketing of a film or game, it gives the audience enough material to decide whether or not they're interested. Whereas if you start vague with some cool looking images, it might interest them enough just to keep the film or game on their radar. It's possible to show some scope, but do it without context and the audience won't be able to put the pieces together; this will effectively tease them as they attempt to make sense of it.