The standard sync function seems to sync applications between my iPhone and Mac (That is, the applications seem to end up on my Mac.) I don't understand the point of this: they can't be run on the Mac, and if I lost my iPhone, I can download them again from the App Store. Is there some way to prevent applications from being synced?
The point is that they can be restored much quicker from your Mac to an iOS device than downloading them again. This may (of course) depend on the number of apps you have on your iOS device and which sizes they are. (Many games and navigation apps are way over 1GB each.)
To prevent app syncing you would just uncheck this box in iTunes while you have selected your iOS device in the sidebar and chosen the Apps category as shown in this screenshot.