If you are using Google Apps premier or Education edition, you can sync your email with Blackberry phones, using BES server, it could be your own BES server or a hosted BES service.
It will sync by default just your "Sent Mail" and "Inbox" folder/label, but if you want other labels to be pushed to your blackberry follow this procedure.
- Open Messages on your BlackBerry
- Press the Menu key
- Go to Options -Email Preferences
- Press the Menu key again
- Select Folder Redirection
- Select the folders you want to to synchronize with your BlackBerry
Use the plus (+) sign to expand labels/folders.
Save the changes and you are done, now all new emails with those labels applied will be pushed to your Blackberry. Because of the way Gmail manage labels, you can have duplicated emails in your Blackberry, as any mail can have more than one label at a time.
Also consider that old email with those labels with not be synced with your phone, and only as new email arrives, or is applied a given label will be pushed to your device.