In terms of wargames, I can’t personally vouch for them since I’m only a dabbler in the genre, but there are quite a few on Android that seem to have decent user reviews.
The most prolific, if you can handle bare bones presentation and interfaces, are John Tiller and DK Simulations, both with dozens of individual titles across various theaters.
Atlantic Fleet and Pacific Fleet are the ones I’ve seen the most praise for as mobile- first wargames, with solid presentation.
And then here are a few more that might be worth a look:
All of the Enhanced Infinity Engine RPGs are available (Baldur’s Gate, Baldur’s Gate 2, Icewind Dale, Planescape Torment). Also Neverwinter Nights, KOTOR and KOTOR 2.
Also, ScummVM is gearing up for a new release soon that will be spiffing up the Android port, so you can play a ton of adventure games.
Final Fantasy Tactics is pretty great on Android. The touch interface isn’t perfect, but it’s livable and the new localization (and very minor new content) in War of the Lions is just as fabulous as it was originally on PSP.
Titan HD is a solid port of the old Avalon Hill board game. It apparently isn’t supported anymore, but it still works on my newish Android tablet. The AI is not great, but it is better than no Titan at all.
Yeah, that’s why included that caveat. Last I checked, they didn’t backport any of the touch improvements to Windows, either- It’s just so much better on Android (and I assume IOS).
3- and 4-player are fairly similar, but 2-player is very different. So don’t be surprised that what you learned to beat a single opponent doesn’t work so well against multiple opponents.
I’m playing it like I play Civ, which is that I do things that look cool, and then when push comes to shove, I spend a bunch of time optimizing a particular system to try to get out of whatever hole I’m in. Turns out, that works for a computer game but not a board game, because all of a sudden the game ends and you don’t have the VPs!