I used to use KGS, but that was mostly on the computer, though I know they also have an Android app. That was several years ago, though. My friend who still plays does so mostly on Pandanet via Android.

Those are both for multiplayer, of course. For single player, a while back I used Gridmaster along with a build of LeelaZero, and there are various apps that offer Go problems, including one my friend likes, but I have forgotten what he told me it was. I think it might be Tsumego Pro, but I’ll have to ask him again next time we talk.

Edit: Dragon Go Server probably deserves a mention as well. That’s a site for, basically, postal games via email, and can be accessed entirely via a web interface. It’s not as popular as the sites with faster time controls, but it’s kinda nice for playing a leisurely game with a busy friend.