The opening shot of A New Hope features a fight in space between the rebel ship, the Tantive IV, and an Imperial Star Destroyer. I understand why the Tantive IV would be (uselessly) firing at the Empire's ship since the Rebels were running for their lives. But why would the Star Destroyer shoot at the Tantive IV? A misplaced shot could destroy the ship altogether. Indeed, at one point they hit the middle of the ship, causing an explosion.
It's my understanding that the Empire was trying to recover the stolen Death Star plans, not destroy them. They wanted to recapture the plans, detain the crew and probably torture them for information on the Rebellion. This is reflected in Vader's commands.
VADER: Commander, tear this ship apart until you've found those plans and bring me the passengers. I want them alive!
Since they were going to capture the Tantive IV in their tractor beam anyway why risk destroying the ship and its precious cargo?