A newbie queston: how do I transfer my data to a new handset?

Hello r/android! I've been a G1 user for a long time, but that's as much as I have been. I haven't delved into the depths of Android, it's just worked.

I've got a few apps on my G1 ('mileage' springs to mind) that I could do with transfering the data over to whatever phone I get next.

How do I do it? What's the best way? Can I USB cable it up and copy some directories, and everyone is a happy panda? Could it really be that easy?

Help me Obi-Wan Kenandroid! You're my only hope!