It took Apple a while, but even podcasts can now be sync'd over the air without iTunes.
The only thing that I really needed to go through iTunes was syncing my iPad address book with Google Contacts (in GMail). I only synced about once a month (probably even less often) so my address book really missed some contacts.
With CardDAV the iPad (or iPhone for that matter) directly goes to Google without the detour through iTunes on the PC. The benefit: you'll be really in sync, like on Android. (SCNR)
Here's what you need to do:
Create a new Account with CardDAV
In Settings find the Mail, Concacts, Calender bullet; the first section is the Accounts section, and there click on Add Account.... Create a new Other account and then select Add CardDAV Accont in the Contacts section.
All you need to provide then is google.com for the server, and your Google credentials (userid and password). You can of course modify the description, but the default - taken from the server name - google.com sounds quite apt, doesn't it.
That's it.
Really.
Unless...
... you did sync your Google contacts previously through iTunes - like I did.
Because then you will notice - in the contacts app - that now all entries are duplicate. Once from the new CardDAV account, and once from the iTunes sync.
Let me show you the fastest way to
Delete the old Address Book
Back to the Settings / Mail, ... page.
Create a new Microsoft Exchange account with dummy parameters like test for Email, Username and Password. I used "test" for it.
Next the iPad will ask you for the services on this account, make sure you turn Contacts to ON.
And now the old local address book will be gone.
Remove the dummy Exchange account you just created.
Now you have all your Google contacts sync'd to the iPad through CardDav... over the air. No iTunes needed.
Don't forget to go to the PC and turn of Contacts sync (to Google) for the iPad as well.