Shows and movies may do this for several reasons: to keep audiences around for longer, production breaks, financial reasons, actors signed on for other projects that interfere with shooting of a season, to ramp up other projects that needed more time, just to name a few.
In the case of Breaking Bad, Brian Cranston indicated that they planned to shoot the first 8 episodes, then take a 4 month break from production with the intent of filming those then having the series air sometime in 2013.
Then you have movies that do it, like the Harry Potter franchise. The reasoning given there was that the final book was so dense with material that trying to fit it all in a single movie, even a super long one, wouldn't do it justice.
The long and the short of it is that there's many reasons for TV shows and movies to have seasons and single movies split into two.