Currently installed on my phone: Golfshot GPS, PGA TOUR, Rules of Golf, SkyDroid, The Grint, and V1 Golf Premium. There's a good chance I'll make the switch from Android to the iPhone in May so I can a hand full of apps that aren't available for Android. While it's not a golf specific app, I do have a Sony Action Cam (AS15) and use it with the PlayMemories app to record my swing at 120fps. 

Team Titleist

GolfLogix

V1 Golf

Tour Tempo

PGA Tour

WGT

I use Who'surCaddy,  it has GPS, course info, tee time schduling  and other features.

I also am  a  "Zepp for Golf " user, Great for the practice tee swing tracing, etc.

Mike

My golf apps are:

Golf Channel <-- for my golf news

Golf Live Extra <-- to watch TGC when a tv isn't accessible

GolfLogix <-- for GPS, course info, training videos, etc.

GolfNow <-- for tee times

Titleist <-- for too many reasons and purposes to list

USGA Rules <-- to prevent fights and settle arguments

I am going to have to check out some of the other great apps everyone has suggested.

Titleist and Golflogix and also going to get more!!

My current golf apps are:

ShotByShot

GolfNow

Vision54

Vision54OnCourse

V1 Pro

Total Game

USGA Rules

Metronome

Wind Meter

Titleist

GHIN

SkyGolf360

SkyCaddie

Eyeline Golf

Golf MTRx

Swing Pro

GolfCoreGrip

There is also a good article on TPI about Golf App Technology.  I thought it was very well written.

Chris

I have the Swing Plane app on both my Iphone as well as my IPAD. 

I have a special container on my iPhone just for Golf stuff

Golf Channel - news

Golf Live Extra - news, live scoring

PGA - news, live scoring

Mobitee - GPS and score keeping

GHIN

Titleist

Ubersense - Golf swing app

The Grint - A new GPS and score keeping app that i just downloaded.  Not sure if it's any better than Mobitee