Seems to me that if all you're concerned about is the apps themselves, then there are two ways to go:
- Right click your device in the iTunes sidebar and pick "Transfer Purchases".
- Go "iTunes Store" in the iTunes sidebar, choose "App Store" on the bar across the top, go to "Purchased" on the right sidebar in the store itself, then click the "Download All" button. This has the same affect as "Transfer Purchases", except it'll get every app you've ever downloaded, not just the ones currently on your iPhone. Thank you iCloud.
Then from there simply go ahead with your sync. Your apps will all be deleted from your phone first, then transferred back to your phone WITHOUT any data and IN THE WRONG ORDER on the home screen.
However, if you actually care about how your apps are set up, what order they're in on your home screens, and the actual data contained in your apps, e.g., your voice memos, your photos, your passwords, documents you've created, etc., then it's just not as simple as the above. Something like wjosten's instructions are necessary, especially steps five, six, and seven.
Of course, if the apps you care about keep all their stuff in the cloud, then maybe this isn't a concern for you. For instance, the Facebook app of course keeps all it's stuff on the Facebook website, so maybe it's not a big deal to log back into the app since all your stuff will of course still be there. The thing to keep in mind is if you use any apps that actually store their data in the apps themselves, not on a website or in the cloud.
I just went through wjosten's instructions and the only issue I encountered is that the apps didn't come across in the same order on my home screens, but all my data came trhough intact, which is what I really cared about. A few minutes of moving icons around I can handle. Losing data I cannot.