Blackberry is popular because it was the first kid on the block. There is absolutely nothing you can't do on a smartphone that you can with a blackberry. In fact todays smartphones are blackberry ++.
Now Blackberry is popular with business users because it allows standard configuration and deployment across a consistent platform. If all of your employees use their own version of the smartphone it would be a nightmare for IT&T to configure. And that is why apple has the iphone configuration utility (and they have been successful with it)
Finally, while Blackberry is infact a device (the car on the road), in normal usage it refers to the entire end to end solution which also involves a server, protocol etc.
I absolutely dont think Blackberry is a MUST. It just happens to be most popular with enterprises.