I backed up my iphone to move it to a new phone all my contacts, notes and calendars are gone. when the iphone backs up does it copy everything? is there a way to get my important stuff back?

note: I didn't check 'sync contacts, notes, calendars' because I was travelling and had to use a different computer to sync our stuff. I assumed 'backup' and 'restore' meant something in this topsy turvy apple worldy. was I wrong?
The backup function backs up all application data, system settings and user preferences. Data such as contacts, notes and calendars are only synced on request unless you are using something like MobileMe which syncs this data in the background.

If you didn't sync your contact, note and calendar data whilst you were travelling then your only backup remains on your primary machine. Restore from there and your contact, note and calendar information will be synced back from whatever applications you have designated as managers of that data.

From my own personal experience I have used and restored from MobileMe independently of iTunes successfully many times and continue to use that service for that reason should an iTunes or system backup ever fail for me. In future this functionality will be available for all via the iCloud service.