Like a lot of people, I have come to rely more and more on mobile applications, and less on desktop programs. I still love my iMac, but the list of things I use it exclusively for (video editing, songwriting, maybe one or two other things) continues to shrink.
One of the by-products of this has been a simplification of my iPhone and iPad app use and flow. Rather than a hundred apps on my devices, stashed away in folders, I have moved towards having many fewer apps easily accessible from the screen.

Here are the 10 apps I use the most. For purposes of this exercise, I’m not going to count the pre-installed apps, like Camera (95% of my photos and videos are now taken with my iPhone), Mail, Calendar, Contacts, Messages and Phone.
Swell

I’ve already covered this great app in detail, so I’ll just restate that I use it all the time, and more than any other app, including the pre-installed apps.
Life360

Largely because Find My Friends, an Apple app for crying out loud, is so completely unreliable, this has become our family’s default and oft-used “where the hell are you” app. It’s not perfect, but it works.
Dark Sky

I’ve tried many weather apps, and this one comes the closest to the balance between minimalist information and useful data. I never use the map, which is what got it on the app map initially, but I like everything else about it. It’s been my weather app of choice for a good while.
Facebook

While not pre-installed, this is the functional equivalent of a pre-installed app. I’m not a heavy Facebook user, but it has all the people and they aren’t coming to me. It’s the virtual water cooler where one must go if one wants to interact with others. I hate, with a passion, the way Facebook keeps jacking around with my news feed (for example, by changing it back to top stories rather than most recent), but there’s not much to do about it (except immediately change it back).
Fitbit

I am a big fan of the Fitbit One. I’ve worn it for over a year, and I check my stats multiple times a day. Seeing that you’ve got your miles in before the last workout of the day (would otherwise occur) is like waking up at 4:00 in the morning and getting to roll over and go back to sleep.
Evernote

I’m not big on entering notes from my iPhone or even my iPad. For all its awesomeness, the Evernote apps- and even the desktop program- are hot messes of too much information on the screen and chaotic navigation. But it has long been my primary file cabinet, and I access stuff all the time.
Spotify

iTunes is a horrible train-wreck of an experience and probably always will be. Spotify is the one and only music application you need. I listen to 90% of my music via Spotify, and the rest via Google Music, which will not increase its share unless it removes the frustrating 20,000 song limit.
Here’s a short little playlist, via Spotify.
Yahoo News Digest

At first, I loved the simplicity of this app. Eight stories in the morning and eight at night. I still use it, though I find that, more and more, I am reading things I already know. But if you want a simple but elegant news app, this is the one.
Feedly

Feedly is the best Google Reader replacement, and in many ways an improvement over my long-lost love. I don’t use it much on my iPhone (the screen is just too small for optimum content consumption), but I use it all the time on my iPad. Reading my feeds is one thing that has moved very decidedly from an iMac thing to an iPad thing.
Dropcam

I have had more than one frustrating experience with Dropcam hardware, but it’s getting better, and I use the app daily all the time to view my various security cameras. I pay for the cloud storage of the video feeds and I like the ability to get alerts when the camera senses motion. As soon as they come out with the long-rumored weatherproof camera, this app will be the only security service you need.
Honorable Mention: Skype (the best way I can effectively video-chat with my teenagers from afar; I prefer FaceTime, but young people seem to prefer Skype), Hue (the hardware is way too expensive, but, you know, colored lights can hypnotize), HBO Go (I use it all the time on my Apple TV- Sopranos FTW), Instagram (last year, it would have been at the top of the list, but it’s fading fast), Kindle (if this were an iPad only list, it would be near the top).