I 2nd Gas Buddy. There can be a 10¢ per gallon (or more) difference on any given day of the week at stations close enough to choose either one, but far enough apart that you can't see both signs to see the prices. I just press the button and see where's cheaper. Or if traveling, where the nearest gas station is (and which ones are cheaper).
I do use Waze, and really like it when I am traveling. We live rurally, but get on a 6 lane interstate to go mostly anywhere (including the kids' school) so if there is a traffic accident closes lanes, it's helpful to know exactly where the accident is so I know where to try to exit or go around.
I use CardStar for my store cards. Not credit cards, but all those store issued member cards so that you get discounts. Most stores can swipe the UPC code directly from your phone screen using that app, or if not, they can read the numbers off of it, without me having to carry a stack of 50 of those plastic cards (or key chain tags) around. That's nice. I've had a lot of people ask me what it is when I whip out my phone at stores for that reason.
I do like Applepay, too. I just wish there were more retailers who supported it right now. It makes payment easier (and actually more secure as well).
I do use digital coupons at my regular stores (Publix, Target, etc) and those are nice. You do all that at home and then just enter your phone number at the time of payment. But, if I haven't updated in a few days (searched for coupons) I can do it right from my phone when I'm at the store as well.
I do use the Notes app (iphone) to keep lists and random bits of information. Gate codes for private entrances that I don't memorize. Dimensions for furniture or windows or whatever when I am shopping for the home. Photos for paint swatches and their brand/color codes, so I can match. Grocery lists, yes. I even put in carry out orders for deli sandwiches... when my husband wants x,y,z on his salad, but if they don't have that he wants a,b,c and my son wants ---- unless they have XXx and then he'd rather have that without the mayo, and daughter wants .... It gets confusing quickly... so I just make a note and delete it after the order is made/picked up.
I hook it up to bluetooth in my car and will use Siri to voice text my kids if I am driving (I'm about to pull into the neighborhood, be ready out front). Or call my mom. Or the pizza place to place a carry out order, so it will be ready.
I don't really use/play any games on my phone. But I do like to check the health app and see if I've been overly sedentary. I use a couple of different running apps to track my actual runs (speed/distance/pace/calories burned, etc).
And I do my fare share of checking FB when I'm wasting time at an appt in the waiting room or whatever.
But overall:
Yahoo Weather
GasBuddy
Waze
GoogleMaps
Waterminder (reminds you to drink water up to an amount you specify)
Passbook (apple pay)
Cardstar
Cartwheel (Target's app)
WalkTrackerPro and Runtastic (my running tracking apps)
Facebook
Those are my main ones.
--
ETA:
You'll also want to brush up on your social media apps if you have tweens or teens. I have a few apps that I only have b/c my teens do, and I like to be able to log in and see what they are up to.
If you are relatively new to this age group, you might know what they are. And it probably varies widely depending upon where you live (what apps are popular among the local kids). Here, they like Instagram, snapchat, and Kik is another one. They don't use FB much at all. It's been taken over by the parental set. LOL