In 2016, Google announced Google Play store support would be coming to Chromebooks. It took a while, but now if you go out and buy a Chromebook produced in the past year you're guaranteed it will support the Google Play store. For those of you lucky enough to have such a Chromebook, you can find more details about using the Play store on your Chromebook at https://support.google.com/chromebook/answer/7021273 .
For those of us whose Chromebooks don't support the Play store, here is a list of web apps you might find useful as alternatives to Android apps:
Utilities:
Offline Notes
Numerics Calculator & Converter
Communication:
Telegram
Skype
Games:
Snes Party - Online Multiplayer SNES Emulator!
Sudoku
Graphics:
Pixlr
Music:
Spotify
Notes:
Selection criteria:
MUST use https.
MUST NOT have intrusive ads.
Do you know of a good web app that should be listed here? Please submit its details in a comment below.