Haven't played Destiny yet? You can now thanks to a free trial for the game on every platform. Bungie provides the details on this trial on a new help article page.
How do I obtain the Destiny Trial or Demo?
The Destiny Trial and Demo are available for digital download. You can find these trial and demo modes on the Xbox Store and the PlayStation Store.

How much disk space is required?
The Destiny Trial and Demo software is approximately the same size as the full retail version of Destiny. See below for approximate download sizes.

The Destiny Trial on PlayStation 4 requires 20 GB of disk space
The Destiny Trial on Xbox One requires 20 GB of disk space
The Destiny Demo on PlayStation 3 requires 6 GB of disk space
The Destiny Demo on Xbox 360 requires 6 GB of disk space

Bungie notes that if you end up buying the full game, your character and stats will transfer over. They say that the demo includes a "sampling" of the character creation, story mission content, and some "cooperative and social activities."