APIs for manipulating documents loaded into the browser. The most obvious example is the DOM (Document Object Model) API, which allows you to manipulate HTML and CSS — creating, removing and changing HTML, dynamically applying new styles to your page, etc. Every time you see a popup window appear on a page, or some new content displayed, for example, that's the DOM in action. Find out more about these types of API in Manipulating documents.
APIs that fetch data from the server to update small sections of a webpage on their own are very commonly used. This seemingly small detail has had a huge impact on the performance and behaviour of sites — if you just need to update a stock listing or list of available new stories, doing it instantly without having to reload the whole entire page from the server can make the site or app feel much more responsive and "snappy". APIs that make this possible include XMLHttpRequest and the Fetch API. You may also come across the term Ajax, which describes this technique. Find out more about such APIs in Fetching data from the server.
APIs for drawing and manipulating graphics are now widely supported in browsers — the most popular ones are Canvas and WebGL, which allow you to programmatically update the pixel data contained in an HTML <canvas> element to create 2D and 3D scenes. For example, you might draw shapes such as rectangles or circles, import an image onto the canvas, and apply a filter to it such as sepia or grayscale using the Canvas API, or create a complex 3D scene with lighting and textures using WebGL. Such APIs are often combined with APIs for creating animation loops (such as window.requestAnimationFrame()) and others to make constantly updating scenes like cartoons and games.
Audio and Video APIs like HTMLMediaElement, the Web Audio API, and WebRTC allow you to do really interesting things with multimedia such as creating custom UI controls for playing audio and video, displaying text tracks like captions and subtitles along with your videos, grabbing video from your web camera to be manipulated via a canvas (see above) or displayed on someone else's computer in a web conference, or adding effects to audio tracks (such as gain, distortion, panning, etc).
Device APIs are basically APIs for manipulating and retrieving data from modern device hardware in a way that is useful for web apps. We've already talked about the Geolocation API accessing the device's location data so you can plot your position on a map. Other examples include telling the user that a useful update is available on a web app via system notifications (see the Notifications API) or vibration hardware (see the Vibration API).
Client-side storage APIs are becoming a lot more widespread in web browsers — the ability to store data on the client-side is very useful if you want to create an app that will save its state between page loads, and perhaps even work when the device is offline. There are a number of options available, e.g. simple name/value storage with the Web Storage API, and more complex tabular data storage with the IndexedDB API.
