Tweetbot - My preferred Twitter app. Multiple accounts and timelines, mute functions, easy switching between lists, Instapaper integration, great search, highly customizable, with traditional RT retweets.
Tweetkeeper - Twitter will only let you download 3,200 tweets at a shot. With this app, you can download all of your tweets from this date forward -- and the tweets of others -- and keep storing them, for a permanent record. I save the tweets of some funny accounts I like, as well as my own.
Facebook - I'd rarely look at my timeline without this.
StumbleUpon - Serendipity in your hand. A way to find the stuff you didn't know you were looking for.
Buffer - With this scheduler app, spread out your tweets, Facebook apps and Alpha.app.net posts so you don't overwhelm your followers.
Alienblue - Makes Reddit less ugly.
Foursquare - A waste of time, perhaps, and an obsessive compulsive addiction, but it pays off when you're in a New York neighborhood and want to find a place to eat or shop -- or remember the place with the great espresso that you stopped in two years ago.
Launch Center Pro - When you have as many apps as I do, it's helpful to have this in your menubar. It can dig deep into some apps and iPhone functions (like using the flash as a flashlight) and take you quickly to bookmarked Web pages. Create an Omnifocus to-do item or a Simplenote or search IMDB with just a few taps. Now if only Apple would let it toggle Wi-Fi.
1Password - Secure access to your sensitive sites; protects your passwords and generates strong ones. If you lose your phone, this important data is encrypted.
TextExpander - Create typing shortcuts for longer phrases and even email form letters. Get a snippet dictionary for commonly misspelled words and words with accents and let this app do the work when you type. Syncs across all devices via Dropbox.
iTransNYC - I don't typically need a lot of help navigating the New York subway, which is this app's specialty. But I do find it useful on weekends or late nights. First of all, believe it or not, the New York subways have a schedule and trains are pretty much on time, so this app can tell you when the next train will arrive on a given line. And it also knows about all the construction detours. I am moving this one back out of a folder where it was hidden, now that Apple has apparently downgraded the Maps application with iOS 6. Updated. 9-25-12
Reeder - When I want to read or share articles from RSS feeds on Google Reader, I use this.
Instapaper - The attractive "read later" app, with integration across all devices. Dark screen mode for low light conditions, attractive fonts, smart suggested readings list. I paid for search.
Flipboard - Turns links from RSS feeds, Facebook timelines and Twitter streams into a magazine format.
Kindle - I have too much invested in Amazon books to use any other app now. I wish it had not been crippled by restrictive Apple iTunes store policies. Another option that lets you buy books directly is the Kindle Cloud Reader, a Web app that can be installed on the iPhone screen via Safari.
Workflow and Notes
Omnifocus - The best getting-things-done project app. Get rid of that gnawing fear that you have something to do all the time. Capture it now and check it off later. Syncs across all your devices (but expensive to buy all versions).
Simplenote - Simple text notes, shared across all devices and computers using Notational Velocity. I put bits of text here when I can't figure out where else to put them.
Bento - A useful database program for projects and staff lists. Syncs over WiFi with your computer.
Dropbox - Easiest way to share files with your computers and other devices.
Evernote - A full-featured, rich sharing app for photos, Web content and more, for sharing across all computers and devices.
Webster's New World - Cheaper than the print version of The Times's official dictionary, and easier to search by typing the first few letters of a word.
Shorter English Oxford Dictionary - In print, this stretches to 20 volumes. Expensive, but cool to have on your phone. Useful for etymological information.
Terminology - A thesaurus-like dictionary of specialized jargon for many fields.
Wikipanion - Fast, easy direct Wikipedia search.
Podcasts and Music
Downcast - I've tried them all, and this podcast app annoys me the least. Streaming, auto downloading, search, an easy interface. Just be careful: Auto downloaded files will eat up your storage and data limits, depending how you configure this. I had a bad surprise when I left 4G downloading on during an international trip.
Spotify - I've tried RDIO, Pandora and many others, not to mention syncing the iTunes library I own. But Spotify gives me the right amount of control, selection and serendipity for music on the go. Stream just about any music out there for $10 a month, on all devices and computers; store some on the app if you're going to be disconnected. Share playlist with your Facebook friends. Good suggestions for new music. With most music I enjoy available here, I spend a lot less buying tracks.
Shazam - Hold it up to the TV, the radio, or the sound system in a public place, and it will tell you the name of that song that you just fell in love with. Still amazing after all these years.
TuneIn Radio - I am a fan of the eclectic music played on KCRW, the public radio station in Los Angeles, and my wife likes to listen to the BBC and a variety of local public radio shows. This app lets you stream these and many other programs from radio stations around the world. It syncs across your devices.
Health and Fitness
Sleep MotionX - An amazing app I use every night. You place it in the bed and calibrate it, then it detects motion to measure your deep sleep, light sleep and wakefulness. It helped me to diagnose my apnea problem, which woke me up repeatedly through the night. Now, with breathing treatment, I sleep through the night. The app alarm also finds the optimal time to wake you up in your sleep cycle. During the day, he app measures daily steps and tells you when you're sitting around too long. And it gives you lots of data in cool charts.
iFitness - Many suggested workout routines, option to save workouts, video demonstrations.
Lose It! - A meal planner and calorie lookup/counter that includes many common restaurant meals and store foods in its database.
Open Table - This is a useful reservation service for restaurants, with menus. I've gotten into a lot of places the day of the reservation.
Dark Sky - Tells you the only thing you need to know about the weather, most of the time: Is it going to rain in the next hour? With radar maps.
Catan - Get your 'Settlers of Catan" fix and hone your skills by practicing against robot players with many types of playing styles.
Everyday - Shoot your picture every day and watch how you change over months and years. If you dare.
Hueless - Mimics an old-style black and white camera, with color filters. Make everything look like the 1930s. Every place looks like a noir film, and everybody looks better in B&W.
Meditate - A simple meditation timer with chimes, with variable settings for preparation, intervals and cool down. It displays a total for the amount of time you have spent sitting, which is not enough, most likely. Take heed. Do not squander your life.