TheGreatOne is correct, but I'll add a bit more information regarding paid apps.

Paid apps are "linked" to your gmail account.  If you were to replace your phone with a different Android phone, and  you used the same gmail account to set up the phone,  you can install the same app on your new phone and will not be charged again for it.

(Say you replaced an Eris with a Moto Droid, or even switched to an android on a different carrier, or upgraded to something new next year.)