Congratulations on your new iPhone or iPad! I've been using iOS for awhile, and I've found that there are many apps I find particularly useful or compelling. Some of them are the usual suspects, and others are a bit more esoteric. Take what you think you'll enjoy. Follow the linked names and titles in this post and you'll end up somewhere you can learn more about the app and get it for yourself.
NB: A list like this has the potential to age very quickly as prices change and app UIs evolve—to forestall that you won't find many screenshots or prices.
I don't really like rain, at least when I'm outside. Dark Sky solves that problem with push notifications when it's about to precipitate. It includes a forecast for the rest of the day and one of the best radar animations I've seen anywhere.
Ita and Clear are two well-designed list management apps on iOS. Make a list. Knock off the things that don't need to be there. Both support iCloud syncing and have nice details, the main difference is in the UI. Clear is brightly colored and has sounds that complement most actions. Ita has Futura and a highly textured interface that shows wear on notes as you use them. It's a matter of personal preference—make your pick.
Letterpress is an addictive word game for iOS. You play until all letters have been used to make a word and the game ends. The winner has the lion's share of the 25 letters on the board. It's free and a lot of fun. Read up on a strategy, you wouldn't want to be unprepared.
Instapaper is great. You put a link in your browser's toolbar on your computer and send links to it all day long. Then you pull out your iPad and plow through all of them in its well-crafted reading view.
I read a lot of RSS, but you may not know what that even means. If you do, great, grab Reeder. It's got the gestures, UI, and integrations you've been looking for. Reeder is available for the iPhone, iPad, and OS X.
99% of the time I use Twitter from a client, and of I'm on iOS I use Tweetbot. It has push notifications and its own aesthetic. It makes good noises too. There are separate versions for the iPhone, iPad, and Mac. Make sure you're getting the correct one.
This is where I find random things while drinking coffee. Flipboard captures a lot of content that I have a passing interest in, so if it's Sunday and I'm being lazy, Flipboard is open.
Evernote syncs notes and so much more. Use it everywhere, and some day some good will come of it. I'm still not sure what that thing is, but it'll be great when it happens. Free.
Someday you'll want to type something on your iPad, and when you do you'll want Writer. It has a nice row of keys at the top that will make your life easier, and it syncs with iCloud and Dropbox.
I like movies, and I like the Netflix app. Free.
Bloom is a coffee timer designed to help deliver consistent results. Bloom lets you set up custom timers and keep track of your ideal weights and ratios.
That's it for now. The second edition of this post was published on 11/20/12.