App Store screenshots are really, really important, if done correctly they can convince more users browsing the store to download your app. Unfortunately so many good apps get overlooked because of bland or poorly designed screenshots. This is not an article telling you how to design screenshots, it's more of an overview of the styles and options that are out there right now.
Some of them are more usable than others, but hopefully you'll be able to use this as a reference when deciding what will work best for your next app.
1. Classic screenshots
When the App Store first launched this was the way all screenshots looked. It's still Apple's preferred method. It's the style Apple use for every single one of their own apps. While I personally like the classic style of screenshot, I don't think it's always the best way to sell an app. Sometimes they can appear a little bland, but this obviously depends on the app. Here's two examples of apps that can get away with the classic look.
2. Flat colour backgrounds with devices
This is possibly the most popular style of screenshot on the App Store right now (if you don't include games). Every other app I see is based on a variation of this design. This style of screenshot will often feature a device on a coloured background with some descriptive text, either above or below the device. I really do like this style. It's clean, bold, and if done correctly can be much more attractive than the classic screenshot. Here's three great examples.
3. Blurred backgrounds with devices
The flat coloured backgrounds from the previous example have been swapped for content specific blurry photos. This style is most common amongst photography, and cooking apps. The Hyperlapse screenshots below are understated and classy, I like the way they've used the same photos in the background. Even though the Over screenshots are based on the same style they look punchier and more fun. These three examples show how flexible this style can be when done well.
4. Tutorial based
App Store screenshots can be a great place to give hints or mini tutorials on how to use an app before the user has even launched the app. This is very smart. It's also especially important if the app uses the phone in a new or different way. Heads Up! is a classic example, it does an excellent job of showing what you're expected to do with the phone. Wake is also a good example by showing how the user can interact with the phone to use certain features. I've never used this app, but I love the look of the "flip to turn off alarm" feature.
A few years ago splitting images over multiple screenshots was pretty popular. Recently I haven't come across many apps that use this style. It's probably because it's a little bit gimmicky and also very hard to get right. Foldify and Headspace both do it really well though.
6. Splash Screen
The first screenshot on both of these examples is like an advert. It doesn't show the app, but instead offers a clear message on what the app is for. As with all these things, if it's done well I think it's a great way to make your app stand out in search results.
Interestingly "IF" uses the last screenshot to show the names of the people behind the app. It's cute, but I think it's pointless to show this on the App Store. If you want to list who built the app, do it in the app. Don't waste a screenshot on it.
7. Photographic elements
I'm a fan of using photography in App Store screenshots, there's just something about seeing the app in a real world setting that I like. It certainly makes it easier to imagine how an app could fit into your life. I have no idea if these lifestyle screenshots convert into more downloads, I'm guessing they don't, but either way both of these apps do it nicely.
8. Mixed orientation
Mixing screenshot orientation really bugs me, it probably should't do, but it does. I think it just looks untidy. I have no evidence to show this helps or hinders download rates (it probably has no effect either way), but as a personal thing for my sanity, I'd say don't do it!
9. AAA games
Indie games tend to go for straight screenshots. AAA titles with IAPs, tend to overlay characters on their screenshots. I'm sure there's a direct link between character overlays and IAPs. 99 times out of 100 if a screenshot has a character overlaid on it, the game will have IAPs. While these all look pretty impressive, they are probably not applicable to the majority of indie developers, especially those building apps (not games). If you do have a game with a character then you should probably use this style.
There's a lack of humour in App Store screenshots, most apps take themselves too seriously, apart from PrismDrop that is. PrismDrop is the only app with screenshots that have actually made me laugh (in a good way). They did such a good job on these that it got a fair bit of press attention, this kind of coverage would most certainly have helped drive some extra downloads.
Trying to be humorous in marketing is very risky and can easily backfire. Think very carefully before trying to do something like this.
Designing App Store Screenshots
However you end up designing your App Store screenshots, just make sure the style is suitable for your app. As long as they look good and convey what the app does you should be all set. If you're in any doubt just go with the trusty old "classic screenshot".
I wrote an article on How to Design Great App Store Screenshots a few years back, while some of the information is now slightly outdated, there's still plenty of solid advice in there. If you're unsure of what's acceptable or expected in screenshots, always check the official App Store Marketing Guidelines from Apple.