Based on my usage of any kind of smartphone, this is my list (might not be complete):
Phone Core:
what I think every smartphone should have, and their (--> specific android apps) I use.
- System Settings
- Phone Dialler
- Messaging (SMS, MMS)
- Address Book ( --> Google Contacts)
- Clock, Alarm, Timer, Stopwatch
- Calculator
- Torch
- FM Radio
- Camera (Photo, Video recording)
- Dictaphone (Sound recording)
- File Manager
- Gallery (Image Viewer)
- Document Viewer / E-Book Reader ( --> Adobe Reader, Kindle)
- Music playback
- Video playback
- E-mail Client ( --> Gmail)
- There is a Gmail webapp.
- Calendar ( --> Google Calendar)
- There is Calendar (Ubuntu Core App), but it does an awful job for Google Calendar.
- There is a Google Calendar webapp.
- Tasks ( --> Google Keep (GTasks))
- There is a Google Keep webapp.
- Notes ( --> Google Keep)
- Internet Browser ( --> Google Chrome)
- There is Browser (Ubuntu Core App)
- Internet Radio ( --> Xiia Live)
- There is uRadio. You have to add stream url-s to it. Playlist files will not work, but stream urls work fine.
- Podcast Manager
- There is PodBird.
- RSS reader
- Weather ( --> AccuWeather.com)
- Dictionary ( --> Google Translate)
- There is a Google Translate webapp.
- GPS Navigation / Maps / Compass ( --> Google Maps, GPS Essentials)
- Platform integrated Sharing and Push Notifications
- Platform integrated Social Media Accounts (user name and password handling in apps and on websites too)
what I would like to use on my smartphone.
Communication:
- Facebook Messenger
- There are multiple Facebook webapps. This one is said to be the best so far.
- Skype, Viber, Google Hangouts
- Google Drive
- There is a Google Drive webapp.
- Copy, Dropbox
- There is a Copy webapp.
- CIBm Token
- Toggl
Games and for fun:
- Google Sky Map
- Go Free, Mouse
- Guitar tuner
- Instagram, Pixlr-o-matic
- Noise Meter
- Terminal
- Call Logs Backup & Restore
- SMS Backup & Restore