The following web-based applications work well across multiple devices from computers to tablets to phones.  Some have available apps for particular devices while many simply run within a web browser.

Assessment Applications:
Infuse Learning
Socrative
Nearpod
Kahoot!
Testmoz
Poll Everywhere
Intel's Seeing Reason Tool
Intel's Visual Ranking Tool

Brainstorming:
AnswerGarden
Padlet

Data Collection and Collaboration:
Google Drive (forms feature)
Evernote

Bookmarking and Curation:  
SymbalooEDU
LiveBinders

Presentations:
Blendspace

Curriculum:
CK-12

Communication:
Remind
Celly
Backchannel Chat
Today's Meet

Classroom Management (Elementary Grades):
Class Dojo

Website Creation:
Weebly for Education

Miscellaneous:
Goo.gl
QR Stuff
A Web Whiteboard