As a retired gamer (just don't have the time or money anymore), who now only plays mobile games, I definitely have thoughts. Here are some games that come to mind.
Modern Combat 5
https://forums.androidcentral.com/e...ameloft.android.ANMP.GloftM5HM&token=Je0EoTGl
The Modern Combat series started as Gameloft's android-answer to the Modern Warfare console games, but it's evolved into a quality gaming franchise in it's own right. 5 is the latest (and there best looking) one, but I've played 3, 4, and 5 and they were all good (1 and 2 were kinda weak). 5 also was the first one to have a really good multiplayer mode.
Shadowgun
https://forums.androidcentral.com/e...d=com.madfingergames.shadowgun&token=GrKgkOzk
Shadowgun reminds me a lot of Gears of War but with just 1 character instead of a squad. Gameplay is very similar though.
Gunman Clive
https://forums.androidcentral.com/e...ps/details?id=beril.mootor.gmc&token=qDuAOoU8
This game was a lot of fun. It reminds me of the old Mega Man NES games. 2D sidescrolling platformer with lots of shooting at stuff.
Deus Ex: The Fall
https://forums.androidcentral.com/e.../details?id=com.squareenix.dxm&token=6QGUdRCc
This was a really good unique Deus Ex game (stealth shooter). It got poor review when it released on console/PC because it's not that good and kinda short, but for a mobile game it's was a lot of fun. (The Dead Space android game was GREAT, and Mass Effect android game was pretty good too, but both seems to have been abandoned. You can't find them through search anymore.)
Age of Zombies
https://forums.androidcentral.com/e...brick.ageofzombies&hl=en&gl=us&token=gOtkakYR
This is a top-down dual-stick shooter. Cartoony but a lot of fun; shooting Zombies is always fun.
Hitman: Sniper
https://forums.androidcentral.com/e...ixmontreal.hitmansniperandroid&token=tEfyFXKT
This is a sniper game with a lot of puzzle elements. I had a whole lot of fun playing it for a while, but it does get monotonous because you basically play the same level over and over with different objectives. That being said, the objectives were different enough, and the variety of sniper riffles was unique enough to hold my attention for a few weeks.
XCOM: Enemy Within
https://forums.androidcentral.com/e...etails?id=com.tt2kgames.xcomew&token=SDEgTx8g
Ok, so this is a strategy game, not a shooter, but it's only one of the best strategy game ever, so I had to mention it. This is a direct port of the PC/console version with the expansion pack. Hours and hours strategy and shooting aliens in the face!!! (No real-time live-action shooting though; it's turn-based strategy. Still, shooting an alien in the face is SO satisfying.)
That's all I got right now, if I think of anything else, I'll let you know.