Although App updates are technically multithreaded and will download in the background, seeing them requires launching the App Store then touching the Updates icon. Also, Apple staggers updates in order to maximize availability of its download servers, so you're unlikely to get updates at any specific time, or at the same time as someone else.
That being said, a bunch of apps have already been updated for iOS 4 and now display "iOS 4.0 Tested" in the description. Here are a couple of the better ones:
Pandora Radio (free, App Store) – Allows you to stream your radio stations in the background after you hit the home button, which is probably on everyone's short list. It's very cool and a must have app.
Evernote (free, App Store) – Features fast app switching, uploading, downloading and recording audio notes in the background.
WordPress (free, App Store) - Fast app switching, optimized for iPhone 4's retina display.
Colloquy - IRC Client ($1.99, App Store) - Multitasking, retina display optimized.
LinkedIn (free, App Store) - Fast app switching.
NY Times (free, App Store) - Fast app switching.
ESPN Score Center (free, App Store) – Fast app switching, but there's no background updating API, sadly.
Fandango (free, App Store) - Fast app switching.
How to Cook Everything ($4.99, App Store) - Fast app switching, multitasking, optimized for iPhone 4's retina display.
Plants vs. Zombies ($2.99, App Store) - Multitasking.
Although some have been updated for iOS 4, there are many more that haven't. Here are some apps I'm looking forward to seeing iOS 4 in:
GoodReader ($0.99, App Store) - It would be nice for it to remember the exact file and location that I was looking at. Uploading and downloading in the background would be nice too. But the new version restores USB file transfer, so I can't complain.
Unfortunately some of the apps most in need of iOS 4 support are still absent. Witness the Facebook app (free, App Store) - which has no iOS 4 support, no iPad support and a "broken UI." They need to get their previous developer, Joe Hewitt back. It will be great when VOIP apps like Skype, Fring and Line2 get on the iOS 4 bandwagon too.
Unfortunately Twitter, IM and IRC apps cannot update statuses in the background due to limititations of the iOS 4 APIs. They can only check for updates in the foreground and that's how it's going to be for a while. The only workaround is via push notifications which can alert you of new messages when they arrive.
What are your favorite/most anticipated iOS 4 apps?