I have my email set up and I am receiving email messages. I have Calendar, Contacts, and Email selected in the account settings for this account, yet contacts and calendar entries have not downloaded.
Just noticed I had to hit the sync button while in the inbox view to get an email that was 15 minutes old.
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Which email app are you using? I use YAHOO and there is a setting in the APP that I have to set for the frequency of receiving emails ... unfortunately the lowest number is 15 mins. You can check out other email apps that have more frequency - I think K9 is one of those that people seem to like.
Do you have background data checked in your data manager?
From your homescreen, hit the menu button > Data Manager > Data Delivery > make sure that background data and data enabled are checked.