As of October 1st 2017, my favorite web apps are:
Trello - http://www.trello.com
Fantastic for organizing thoughts, todo-lists, and everything else. With apps for Android and iOS.
Clubhouse - http://clubhouse.io
Great project management for software companies.
GitHub - https://github.com
The best online Git respository site.
Dropbox Paper -http://paper.dropbox.com
Fantastic tool for writing and sharing notes.
Microsofts Live.com - http://live.com
Basically a free (web-based only) version of Office 365.
I recently ditched my full Office 365 subscription in favor of this. So far I am not missing anything.
Exchange online (part of Microsoft Office 365) - http://office.com
Hosted e-mail for your own domain names.
StackEdit - https://stackedit.io
Great markdown text editor in the browser - which means spell check included.
SmarterTrack - http://smartertrack.com
Hosted customer support system.
I have tried many different tools in all these categories over the years, and I can highly recommend all of the above over any competitors that I know of.
If you know of any better alternatives please do tell me in the comments below - always looking for better toys :-)