Most modern phones can do that - my SE K750 could do it, although the interface was about as elegant as an elephants bum for emails, and the calendar wasn't much better.
I have a
Palm TX and a Nokia N95 8G and both work great. The Palm works through Missing Sync software and the Nokia uses iSync (and a plugin from Nokia)
For e-mails, I presume you mean the ability to download e-mail rather than copy each message over to the phone/pda. If you want access to them all, you probably need to access your email through a web browser.