Pulse: An RSS reader which makes it easy to subscribe to, organize and navigate feeds. Try it out and you'll never want to bother with using a browser to surf for news again.
Tweetbot: I've only recently gotten into Twitter, and I mainly use it to aggregate the blogs that I read. It seems that the blogs that I like put a lot of interesting content up on Twitter which they consider too minor to note on their blog. Tweetbot's tight integration with services like Readability and Instapaper are huge assets for my usage.
Instapaper: Speaking of Instapaper, it allows you to save an interesting article, strip out the annoying ads, formatting and page jumps, tweak the text formatting to your liking, and read it later online or offline. This is less of a killer app now that Safari has a built-in Reading List and Reader mode, but it still has some perks.
TuneIn Radio: Just about the only streaming radio app you'll ever need. Thousands of radio stations from all over the world, advanced features like caching (ie, you can pause your radio!) and recording.
Elements: A simple and elegant text editor that syncs with a Dropbox account. I mostly use it for taking notes, go back to my desktop and my notes are already waiting for me.
Dropbox: Might not be necessary anymore with iCloud, but there are still more apps out there that support Dropbox than iCloud. And until developers catch up, Dropbox will be the easiest way to move files on and off your device. Between all your devices, really.
iTeleport: There are about a million remote desktop app out there with various strengths and weaknesses. I went with iTeleport early and I find it has a good interface and serves my needs. By installing a small utility on your desktop, you can easily remote desktop to your home PC through your gmail account without the need for any messy network configuration.
Let's move on to some games, shall we?
Ascension: An excellent deckbuilding game, faithfully converted into a videogame. It's not perfect, the interface can be a little clunky, it doesn't support fast app switching, and the AI can sometimes get bogged down, but it does have a flawless autosave and asynchronous multiplayer in up to six games at once. I can't stop playing it.
Pinball Arcade: For me, 2012's GOTY is already here. Farsight, developers of the excellent Pinball Hall of Fame series, are launching their next pinball sim on every platform imaginable, and they started in February with iOS and Android. There are some issues to smooth out, such as Facebook leaderboards but no Game Center support, but this game has it where it counts: Pains-takingly recreations of authentic pinball tables. Not just a rehash of previous sims, either, Farsight now has licenses for Bally and Stern tables, which should put just about any pinball table within their reach. There's still a ton of secondary licensing to be secured, but the fact that Ripley's Believe It or Not is already available suggests that ultimate classics like Addams Family and Twilight Zone are not impossible.
Super Crate Box: This may be the perfect arcade game. You just need to collect crates and stay alive, but each crate changes your weapon, and if you fail to kill spawning enemies fast enough, you'll quickly become overwhelmed.
Ravenmark: This is an incredibly good turn-based strategy game. Not only is it beautiful and polished, but it actually managed to create some strategy mechanics I've never seen before. Sure, units have a rock-paper-scissors advantage over each other we've seen many times before, but the way you manage them is really unique. You can group units up into formations to make them more powerful, or split them up to make them more mobile. You can issue standing orders (advance, retreat, pursue) to conserve your command points. All combat is resolved after orders are issued, so you really have to plan ahead. All your schemes can fall apart if an enemy unit gains intitiative before yours does and simply isn't there.
Waking Mars: Finally a martian xenobiology game! In Waking Mars, you're part of the first manned mission to Mars, sent to investigate signs of life found in a cavern. This is one of the most atmospheric games on iOS and it will have you solving ecology-based puzzles to unravel the mysteries of Mars. I dare not say more.