They most certainly do! I download music on my iPhone all the time and never have a problem syncing with iTunes.

In the store folders you should have a folder named "purchased on Joes iPhone".

If the music is purchased from the iTunes store yes, but if you bought a cd, ripped it to the computer, put it on the iPod, and and then had a hard drive failure on your computer, there is no built in way to get the music back on to the computer from the iPod/iPhone.

David, thanks for the tip about the stores folder of purchased.

I see it in "purchased" on my IPhone when connected to my computer, but not it the Store purchased through my computer?

Got this resolved.

Here is a very cool app. If you have Carbonite backup on your computer you can download the carbonite app from the apps store for free and log in and access any file on your home computer that has already been backup up to Carbonite from anywhere. You can download music and play it, pictures and any document it seems and email to someone from your iPhone.

Oh, I also bought at the ATT store an external battery case called a Mophie, you charge it, slip the iPhone in it and it supposedly triples your battery time. It uses it's battery first, then the phone's battery, it will charge your battery phone and you can keep it in your car for when you need it. $90 with tax, but worth it to me. http://www.mophie.com

I love my Mophie... it is a little bigger then the phone but it keeps my battery charged all day and I recharge at night.