Here is my list, not all necessarily for business..
Voice Memo (the name explains it all).. turns your phone into a traditional voice recorder.
Dragon dictation.. allows you to take notes by talking into your phone
Awesome Note: The best note taking app. Allows you to back up to evernote or google docs. Also organizes your notes into folders.
Tweetie2: A much better app for twitter then twitterific or tweet deck, especially if you need to manage multiple accounts. Allows you to see what’s going on around you, track and save searches, make new lists and view lists, tweet from multiple accounts, see who you follow and if they follow you and sync with multiple other applications.
Bump: Quickly exchange your contact info with other apple users.
Remote: Allow you to use your device as a remote for itunes on a computer, your apple TV and more
IM +: Let’s you manage multiple IM accounts at once.
Gorillacam: Gives you a timer for your camera, so you can walk away and take a picture. Other fun camera apps: phanfare, PanoLab, iDoodleIt, PS Mobile
Sushipedia: If you love sushi this will help you discover new ideas for ordering. Just enter your favorite food types and it will show you similar recommendations.
I am Empowered: Offers articles about what is going on in the world from multiple sources. Ran by the Urban League.
WaveBoard: Google Wave for iPhone users.
notifo: for push notifications
StylishGirl: An app for any girl (or guy) who has a ton of clothes and wants to swipe through photos of them quickly.
Some of the obvious social network apps: Flickr, Facebook, Google, LinkedIn, Myspace, Last.fm, 43 Things, Strands
Dropbox or iDisk: Lets you sync files/folders on multiple computers or devices.
Air Sharing: Share files wirelessly
Translator: The name explains it.
IfFoundPlus: Let’s you create a wallpaper that has a number/email in case your phone gets lost. Don’t forget to set your iphone/ipad to auto lock! You store too much personal stuff on there not to.