How can I store Android apps on my SD card? I just got my 3rd Android phone, the problem is that I must reinstall all my applications every time I get a new phone. Is there any way to store the apps on the SD card so that I can insert the new card and all my apps are there?

I would prefer solutions that don't require rooting the phone.
This is a feature that requires Froyo, so unless you have a Nexus One you'll need to either root your phone (which you've already said you don't want to do) and install a Froyo ROM or wait for your manufacturer/carrier to issue you Froyo in an update.

Either way, moving apps to your SD card is pretty straightforward. Go into Settings, then Manage Applications. There you should have the option to move your apps to your SD card.