Pair Your BB with an other phone using bluetooth (I used an android one).
If You have Italian Language Menu (like me)
Go in, "Gestione Connessioni" > "Opzioni Bluetooth" > Select the paired phone or pc > "Trasferisci Rubrica"
If You prefer English Language Menu
Go in, "Manage Connections" > "Bluetooth Options" > Select the paired phone or pc > "Transfer Contacts"
In this way the BB will send to the paired phone / pc a file Phonebook.vcf with all Your contacts.
You can then import this file in gmail from the pc for example or use it for other tasks, since it is a text file that You can read and edit with a simple text editor.
Probably should work for other BB models.
Edit.
I did the same procedure for a BB Bold 9900 ant it works flawlessly , the difference is that with this phone it creates a vcf file for every contact entry.
Bye