PCalc and Simplenote are replacements for the built-in Calculator and Notes apps. I wrote extensively about Simplenote here, and I recommend PCalc very highly as well.
I love Apple’s Remote app. I use it with my Apple TV all the time. “Mint” is a shortcut to the Mint web stats for Daring Fireball. I’m a baseball fan and MLB’s At Bat app isn’t just informative, it’s a really well-designed and well-made piece of software. After the Yankees win the World Series in October, I’ll probably replace it with the Voice Memos app.
I’ve got two and a half Twitter clients on my home screen. I use Birdfeed so much I’ve got it in my Dock. But I use Tweetie too, depending on my mood. Birdhouse is a wonderful “notepad for Twitter”, but I’ve included it in this screenshot mainly because Adam Lisagor is a sensitive young man and I know his feelings would be damaged if it weren’t there.
For what it’s worth, I’ve got the double-click-on-home-button gesture assigned to open the Camera app.