Brain is a library that lets you easily create neural networks and then train them based on input/output data. Since training takes up a lot of resources, it is preferred to run the library in a Node.js environment, although a CDN browser version can also be loaded directly onto a web page. There is a tiny demo on their website that can be trained to recognize color contrast.
Educational web app that lets you play around with neural networks and explore their different components. It has a nice UI that allows you to control the input data, number of neurons, which algorithm to use, and various other metrics that will be reflected on the end result. There is also a lot to learn from the app behind the scenes - the code is open-source and uses a custom machine learning library that is written in TypeScript and well documented.
Probably the most actively maintained project on this list, Synaptic is a Node.js and browser library that is architecture-agnostic, allowing developers to build any type of neural network they want. It has a few built-in architectures, making it possible to quickly test and compare different machine learning algorithms. It's also features a well written introduction to neural networks, a number of practical demos, and many other great tutorials demystifying how machine learning works.
Land Lines is an interesting Chrome Web experiment that finds satellite images of Earth, similar to doodles made by the user. The app makes no server calls: it works entirely in the browser and thanks to clever usage of machine learning and WebGL has great performance even on mobile devices. You can check out the source code on GitHub or read the full case study here.
Thing Translator is a web experiment that allows your phone to recognize real-life objects and name them in different languages. The app is built entirely on web technologies and utilizes two machine learning APIs by Google - Cloud Vision for image recognition and Translate API for natural language translations.
DeepForge is a user-friendly development environment for working with deep learning. It allows you to to design neural networks using а simple graphical interface, supports training models on remote machines, and has built in version control. The project runs in the browser and is based on Node.js and MongoDB, making the installation process very familiar to most web devs.