* F-Droid
This is an obvious one, F-droid is an open source app store, it can also work peer-to-peer, so you can use this to install all the other apps on other peoples phones with no internet.
* Kiwix
Offline wikipedia reader, lets you download wikipedia
* Osmand
Offline mapping, lets you download maps
* Briar project
P2p "store and forward" messaging. Messages are encrypted and people can carry a message between communities.
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Are there any apps you'd want to have available if there was a very long term internet outage? I imagine if that happened apps wouldn't be a very high priority, but it's something simple that can be done pretty easily.
Offline Wikipedia
HTTrack for any wiki I found useful.
Calibre (for the l*gen files)
A dictionary software.
A backup full of the software programs I normally use (VLC, Office, Linux ISOs, Firefox, ...)
At the time, that was pretty much it. I did not have any phone, and only a few apps are useful online. Maps being one because of the smaller form factor and the GPS module. I went to Cuba once, and the only use I got out of mine was maps, camera, and Spanish dictionary.