Setting up Google Mail works well, but the calendar doesn’t always sync. This is an intermittent issue reported on this thread, and reported in KB33458.

About the fifth entry down in the thread is a workaround that worked very well for me, steps repeated here for convenience:

1. Remove the previous gmail accounts.
2. Click on the Add Account button.
3. Click on the Advanced button.
4. Select “Microsoft Exchange ActiveSync”.
5. Enter a description.
6. Enter “m.google.com” in the Domain field.
7. Entered my full email address in the “Username” field.
8. Entered by full email address again in the “Email Address” field.
9. Entered my password in the “Password” field.
10. Entered “m.google.com” in the “Server Address” field.
11. Left the port set to the default (443).
12. Left “Use SSL” set to “On”.
13. Left “User VPN” set to “Off”.
14. Left “Push” set to “On”.
15. Click on the “Next” button at the top.
16. Make sure email, calendar and contacts are set to “On”.

I see some wonderful irony in using a Microsoft protocol to connect a BlackBerry with a Google service.