This app was mentioned in 7 comments, with an average of 1.86 upvotes
This is the version that is optimized for NVIDIA, if you don't have an NVIDIA chipset you will want this version https://play.google.com/store/apps/details?id=com.madfingergames.shadowgun also 99 cents.
Shadowgun isn't free (but sometimes it goes on sale), and it is third person. It is a must play though, and it satisfies all my run and gun urges.
Linkme: Corpse Party Blood Drive EN, The School: White day, Chaos Rings 3, Grand theft auto: vice city, Max Payne, ShadowGun, Ravensword: Sadowlands 3d RPG,
Corpse Party Blood Drive: A sequel to its PSP titles so if you wanna play that you'll need to beat the first 2 games on PSP.
The School: White day: A great horror game which came out years ago so they ported it to Android as a HD remake.
Chaos Rings 3: If you don't know what Chaos Rings is then you must of been living under a rock.(Best JRPG on the Play Store)
GTA Vice city: My personal favorite of the series.
Max Payne: Another rockstar game that came out years ago.
Shadowgun: Madfinger games only good title.
RavenSword: An open world RPG kinda like a skinned down version of Skyrim. (maybe)
And that's all I can think of right now I'll edit it if I see or remember more.
EDIT: Looks like it linked the wrong Shadowgun here is the right link: https://play.google.com/store/apps/details?id=com.madfingergames.shadowgun&hl=en
Shadowgun is a classic https://play.google.com/store/apps/details?id=com.madfingergames.shadowgun&hl=en
Dead Effect 2 is offline and has controller support https://play.google.com/store/apps/details?id=com.badflyinteractive.deadeffect2
Slaughter https://play.google.com/store/apps/details?id=com.venomizedart.Slaughter
Slaughter 2 https://play.google.com/store/apps/details?id=com.venomizedArt.Slaughter2
Modern Combat 4 https://play.google.com/store/apps/details?id=com.gameloft.android.ANMP.GloftM4HM
M.U.S.E. - I know it's a third person shooter :3 https://play.google.com/store/apps/details?id=com.ayopagames.museandroid
Epoch 2 - I'm not sure about this one, I don't have it yet, but people said it has gamepad support ,-, https://play.google.com/store/apps/details?id=com.uppercut_games.epoch2
Neon Shadow has gamepad support and is offline too https://play.google.com/store/apps/details?id=com.crescentmoongames.neonshadow&hl=en
You can also download Octopus app to map your gamepad without root and play games which have no gamepad support. https://play.google.com/store/apps/details?id=com.chaozhuo.gameassistant
Some paid shooting games with no gamepad support:
Deus Ex: The Fall https://play.google.com/store/apps/details?id=com.squareenix.dxm
Modern Combat 3 https://play.google.com/store/apps/details?id=com.gameloft.android.ANMP.GloftM3HM
This is the one that is specifically single player.
https://play.google.com/store/apps/details?id=com.madfingergames.shadowgun
Then try this out. I remember playing it on my Nexus 7 and was quite fun.