I have a couple of apps I'd like to recommend:
First, for managing the family calendar, shopping lists and to-do lists, I've found nothing better than Cozi. There are a number of apps that do one or two of these things really well, but Cozi does them all at least well enough that I have abandoned the alternative apps I once used. The calendar, in particular, is really where it excels. Have all your family members install it and log in using the same credentials, and you have convenience at your fingertips.
I think I already mentioned it in a previous thing, but My Fitness Pal is also a fantastic all-in-one app for maintaining a healthy lifestyle. It is completely free and tracks weight, food and exercise, adjusting your daily "allowed" calories accordingly depend on your goals. It also has a (slightly clunky) recipe nutrition calculator you can use to save frequently made meals into your own personal database.
When I had a newborn, the Total Baby app satisfied my need to document everything. We used it religiously the first four months of my daughter's life to track diapering, nursing, sleep and doctor visits, up until she started daycare. I still keep it installed on my phone (she's now four), for nostalgia and also because we still use it to track her vaccination history. (Amusingly, according to the app today, it's been 1,464 days since she has eaten, slept or had her diaper changed.)
A few other apps I use frequently include The Weather Channel, AP News, Care Care (documents gas/service history), Kids Media and BigOven. I think I paid a fee for it, but I also highly recommend (for women) the app P-Tracker for keeping track of period cycle/fertility. The future prediction calendar is also invaluable for vacation planning!