As you may have already seen, I am a contribuitor to openstreetmap.
I believe that maps shouldn't be owned by a big corporation so I do my part on fighting against that.
Openstreetmap is a community project just like wikipedia where anyone can contribute (which... being totally open can lead to vandalism [1])
[1] Vandalism on Openstreetmap
These are some tools I use (or plan to) on my mapping activities
Vespucci is a great tool for more in depth mapping on android, it supports a bunch of functionality and allows you to do basically anything as if you were on a computer (with the added restraint of being in a limited screen size that is)
If you wanna contribute to the map without knowing much about OSM itself then this application is for you! It allows you to answer "quests", letting you complete data on the map without having to worry about what tags to use or which syntax to follow
StreetComplete homepage (HTTPS)
JOSM is a super powerful tool, one of my favourites and my go to when I'm in the desktop/laptop. If you can't map it with JOSM then you may not be lucky with any other tool.
While I don't use this one, I'll leave a mention to it as it is the entry gate to most armchair mappers. It's a browser based editor, not as powerful as JOSM, but has a nice interface and is quite intuitive to use
iD editor on openstreetmap website (need an account, HTTPS)
I'm also curious about trying FieldPapers, but I haven't really found a printer to use it and seems kinda "old school", still, may be less fiddly than using a smartphone.
FieldPapers let's you generate guess what... Field papers! Like small squares of the map that you can print and takes notes on