Is there a way to sync Address Book contacts added from an iPad, on iPhone and Mac without having to manually sync with a USB cable and through the Mac?
You can host your own calendar (CalDAV) and contact (CardDAV) server using Mac OS Server ‘Leopard’ or Server ‘Snow Leopard.’ These will sync over the Internet to iCal and Address Book on your Macs, and to your iOS devices.
If you don’t want to get an expensive Mac Mini Server you could go with using an old retired notebook or even a virtual machine with a Linux installation. The open source project DAViCal will provide you with both CalDAV and CardDAV services.
I am personally using an installation of DAViCal too keep my Macs and iOS devices in sync using a older machine I have at home as the server. I would recommend this solution as you remain in control of your own data. Getting it up and running requires some work, but you would be able to congratulate yourself with the accomplishment. There are step-by-step tutorials for setting up both Linux and the DAViCAL software available.
With Snow Leopard's address book, you can sync you computers contacts to your gmail. Go into address book preferences/accounts and then choose the option to sync with google. See this link on how to do that. http://docs.info.apple.com/article.html?path=AddressBook/5.0/en/21507.html
Then on the iPhone or iPad go into settings/mail,contacts,calender and set up ur gmail as Microsoft Exchange. See this link on how to do that. http://www.google.com/support/mobile/bin/answer.py?answer=138740
There are a number of options, these solutions assume you want to sync your contacts to Apple's Contacts.app on your iOS device and not a third party app.
Apple's service is the most straight forward (it should just work) and offers other benefits such as storage.
iOS devices can use Microsoft's Exchange protocol to update the device's email, calendar and contacts. If you are running Snow Leopard you can use also connect your Address Book, iCal, and Mail to the same exchange server and your contacts will sync between your iOS device and your Mac's Address Book. A free option would be to use Google sync on your iOS device which uses Microsoft's exchange protocol. However Google Sync doesn't work for desktop applications like Address Book right now. So you would have to find a way to sync your Address Book contacts to Google which is possible.
Here is a useful guide about syncing contacts between iOS devices. I used to have MobileMe set up and used it in combination with the Address book. I am on a Windows PC now and manage my contact through Windows Contacts for my PC a third party app to transfer contacts between my iPhone and iPad 3 (I currently do not use the same iCloud account for both).
You can sign up for Apple's MobileMe service. It is $99/year and is the only option (AFAIK) for what you want to do.