Do I need to purchase them separately for every iPad I have?
As long as you log in on both iOS devices with your same login from Apple (or backup and install them with the same login on your Mac/PC with iTunes), you will be able to use the same apps and other data without the need to purchase them again.
You can still manage your apps separately for each device: For instance, iTunes will keep them apart (you get to name each device yourself), and you can install different sets of apps and photos, music and all on the devices. But anything that comes from the App Store is linked to your Apple ID login - and once you've purchase something with your ID, you can install it on all your devices.
I'd also like to add some info.
In iOS 5 you can set your devices to automatically sync new apps. This means that they will appear on all your devices once you have bought them. (However, this does mean several devices will start downloading apps as soon as you purchase them, and therefore use up considerable bandwidth, and a fair portion of your data allowance)
This can be set for music and other stuff you buy in the itunes store. Unfortunately this does not work for songs you add manually.
There is an alternative, for some files you can use dropbox or a similar service to transfer the data between your devices. But that is not syncing anymore.