A patent can be fairly broad if it meets the requirements, two of the most important being novelty and non-obviousness. However, it is difficult for an idea to be broad and still meet the requirements.
Let's use the Blackberry example. Blackberry almost certainly has some specific patents. But smartphone is way too vague. The desirability for something to be smart is obvious.
What about wireless text messaging? HAM radio operators were sending wireless text messages in the 60s (my father had a setup). So, this fails the novelty requirement, already been done.
Next, consider: text messaging via cellular wireless. You might be able to patent this, but whoever invented cellular technology probably already considered it and beat you to it.
Need to be more specific ... It would take some research, but I am guessing that Blackberry has a patent for a specific messaging system, i.e, protocols for sending, receiving, and storing messages. But, that won't stop someone else from developing their own messaging system.
Finally, note that in a highly competitive, profitable business such as smartphones, there are many patents, and the patent owners will often believe that another patent is in conflict with theirs. Legal battles can take years to resolve.