These are Chuck's recommended, almost indispensable, apps. All apps are available from iTunes, comments are based on experience with the iOS platform. Availability and experience on other platforms (e.g. Android, Windows Phone, BlackBerry) may vary. Please check prices, many are free, but others are not and / or have in-app purchases.
Productivity
Evernote - benchmark note-taking app, has tons of extensions and uses to explore
StockTouch - a great visual way to see how the market and your particular stocks are doing.
Pepperplate - my (Chuck's) favorite recipe aggregator. Build and manage your own cookbook based on your favorite recipes from any source - load them via a website, access them via the app.
Grocery IQ - make and manage your grocery lists here, sorting the foods automatically into the aisles they're in, and even setting up the order you'll encounter them in your stores. Genius.
Deliveries - if you buy a lot of things that require tracking numbers, you can track them all here easily.
TRAVEL
Waze - GPS and route-tracking, still the best at figuring out the quickest route from point A to point B based on real-time conditions.
Kayak and Hipmunk (separate apps) - tag-team these to find the best flights. Hipmunk gives a great visual look at flight schedules, layover durations, etc...., but Kayak captures more airlines.
TripIt - aggregates your flight, hotel, rental car information to put all the details together for your trips.
TripAdvisor - the best "mature" review and travel recommendation place around, it's not going to tell you that Subway is a great restaurant.
Living / Entertainment
NextIssue - if you love magazines, you need this app. Access to over 150 popular magazines for a flat price of $10/month, or add a few weekly periodicals (such as SI, Newsweek, People) for $5 more. Read as many or as few as you want. (Hint: if you like cooking, subscribe to all the cooking magazines, find recipes you want, then use Pepperplate to import them into your collection.)
Spotify - Spotify has a huge music catalog, lots of mixes, and with a paid subscription, pretty much everything you could ask for in a music service with selection and options.
IMDb - great for learning about movies and TV, including showtimes, theaters, etc....
Instapaper or Pocket - very similar services, they allow you to save articles from the web for later off-line reading.
GolfLogix - the most broadly-featured golf app I've found, allows you to set tee times, keep score on the course, and analyze your play after the round.
GamES
Elevate - brain training. Every day you'll have 3 games, which will make you think, listen, and process information. Recently named 2014 Game of the Year by Apple, it is fantastic and beneficial.
Candy Crush Saga - Shelley's current game of choice, good for 5 or 30 minutes at a time.
Threes - simple to learn, hard to master, again it's a quick brain-exercising time-killer.
Duet - need to work on your hand-eye coordination? This beautiful and elegant game is for you.
Battle Supremacy - tanks, fantastic physics and graphics, and war, with single- and online multi-player modes. I needn't say more, except that it's very well-executed.