See also: Android apps I like

These are the Chrome extensions I currently use.  My favorite ones are boldfaced. [Now gradually adding links to Firefox versions.]

• BuiltWith Technology Profiler [Firefox]. Find our what the website you are visiting is built with.
• Chrome Remote Desktop. Access other computers or allow another user to access your computer securely over the Internet.
• Diigo [Firefox]. Highlighter & post-it notes, bookmark & archive.
• Discard Draft Keyboard Shortcut. Discard draft button shortcut key in gmail.
• Explore nearby places for Airbnb. Explore must-see places around your Airbnb listing, see exact distance with a short description of popular
• Facebook Purity.  Cleans up and customises Facebook.
• Feedly [Firefox]. News reader with seamless migration from Google Reader.
• Gmail ‘Expand all’ keyboard shortcut. Press Alt+A to expand or collapse a Gmail thread
• goo.gl URL Shortener [Firefox]. Seamless use of Google URL Shortener.
• Google Docs. Create and edit documents.
• Google Docs Offline.
• Google Hangouts. Chats and video calls.
• Google Sheets. Create and edit sheets.
• Google Slides. Create and edit presentations.
• IMDb and Rottentomatoes info. Show Rotten Tomatoes movie ratings on IMDb.
• ImprovedTube. Set default playback speed, screen size, video quality, and more.
• Instapaper. Saves links for offline reading.
• Last.fm Scrobbler. Scrobble from YouTube and many other websites.
• LastPass [Firefox]. Free password manager and form filler.
• Mailvelope.  Enhance your webmail provider with end-to-end encryption.
• Momentum. Replace new tab page with a personal dashboard featuring todo, weather, and inspiration.
• My IMDb. Highlights the movies you’ve already seen (voted for) when searching IMDb or displaying actor/director pages.
• Nanny for Chrome. Blocks access to specific sites.
• News Feed Eradicator. Disables Facebook’s news feed.
• OkCupid Enhanced. Improves OkCupid in a number of ways.
• Pomodoro. Pomodoro Technique implementation.
• Pushbullet. See phone notifications and send SMS from your browser.
• Rearrange tabs. Lets you rearrange tabs using keyboard shortcuts.
• Right Inbox for Gmail. Schedule emails to be sent later.
• RSS Subscription Extension. Adds one-click subscription to Chrome’s toolbar.
• Shut up. Disables comments on Facebook, blogs, and most other sites.
• Spreed. Read faster.
• Tab pinner. Pin or unpin tabs easily using keyboard shortcuts.
• Time Tracker. Keeps track of how much time you spend on various web sites.
• Timer. Creates a browsing session timer for a specified time and notifies the user when the session is about to be over.
• Toggle Switch Recent Last Tabs. Toggle between your current and last used tab with a keyboard shortcut.
• uBlock Origin. A fast, potent, and lean ad blocker.
• Unlimited Free VPN. Access websites blocked in your country.
• Vimium. Provides keyboard shortcuts for navigation and control in the spirit of Vim.
• Vysor. Control your Android phone from your computer.
• WasteNoTime. Blocking time-wasting sites while you are working.
• WorkFlowy. A beautiful tool for lists and notes.

With thanks to Tom Ash, James Ting-Edwards, Peter McIntyre and Ryan Carey for valuable suggestions.