It really depends on what you like.
The apps I use most are: (1) the one from my bank that allows me to deposit checks from home (has me take photos of both sides of the check). Saves me trips to the bank. (2) the Walmart savingscatcher app. I take a photo of the QR code on the sales slip when I get home and it checks for savings at other stores on items I bought, giving me any difference. Also, it allows me to throw away the receipt as I have a copy in my phone if I ever need to return something. (3) free games. The ones I use most are Castle Story, Dragon Story, and Solitaire. (4) Wunderlist. My shopping list for each store is in my phone.
I always read the reviews in the app store before making a decision to get an app. I noticed one app that had 5-star reviews up until December of last year, at which point it went to 1-star reviews because of a buggy update. Check out the "favorites" list too.