I am using HTC Wildfire handset, but I think following question applies to all Android-based handsets.
My Google Account has been added under
Settings -> Accounts & Sync --> Google (under Manage Accounts)
When I click on "Google", I get following options
Sync Contacts Sync GMail Sync Calendar
In Accounts & Sync option, I have turned off (unchecked following options)
Background Data Auto sync
NOTE: I have turned off Background Data, and Auto Sync before adding my Google Account.
I want to get apps and games from Market, but I don't want to sync any of my Google Account data with my phone i.e., there should not be any traces of my Google Account in my phone.
How can I do it?