Can I sync an iPhone to multiple computers without erasing all the applications?
It is really annoying, isn't it.

One thing that works reasonably well is for you to right click on your device in iTunes after connecting it (but before syncing it) and select "Transfer my purchases". That will copy your apps to the local copy of iTunes, so if it syncs it won't wipe things out. Not for apps at least. Music and video is a whole other headache.