A list of things I regularly use or reference and think are awesome. Any tools mentioned are not necessarily ones that I use in my day job and are solely my own personal preference.

UI Development
Codepen is a great way to rapidly try out and present UI concepts. Often I will create pens to figure out small, isolated components.
The HTML Living Standard is a great way to keep up to date with evolving HTML specifications and is an invaluable reference when discussing semantic markup.
The Web Accessibility Guidelines are a vital reference and the web would be a better place if we all referred to this more. Making our content accessible is something I would consider a developer's professional responsibility.
Web Accessibility Colour Contrast Checker is a great tool to simplify choosing human-friendly colour combinations for our sites and applications.
CSS Tricks is a great way to keep a finger on the pulse of a rapidly growing and ever-changing field. There are many famous articles on this site relating to front-end development.
Visual Studio Code is more and more frequently becoming my text editor of choice for any non-server side work. If I'm working on .NET projects then I still tend to prefer it's more fully featured older brother, Visual Studio. However VSCode is a powerful, lightweight and fast program which I enjoy using on a daily basis.
General Web
The MDN docs are essentially the magnum opus of web developer resources. Whether you need to remind yourself of how to create a dropdown component, or how cross-origin resource sharing works - the moz docs have you covered.
Codewars is a fun way to practice your programming skills. There are many sites like this however I have found this one to particularly fun.
Server-side Development
Visual Studio is currently my IDE of choice when working with server-side code. It's debugging features alone are fantastic. It is a powerful piece of software that makes building web applications easier and easier with each update.
Postman is currently my program of choice for testing REST APIs I'm working on.
Swagger is another way I like to test REST APIs I'm working on. In combination with Postman it can rapidly speed up development.
Fiddler is a great tool for HTTP, traffic and proxy related debugging.