In The Elder Scrolls V: Skyrim for the PC, PS3, and Xbox 360, there is some debate as to what is better, The Black Star or Azura’s Star.
Both of these special soul gems can trap any size of creature, and is never broken or consumed when you fill an item with it, essentially giving you infinite grand soul gems, however The Black Star is only supposed to trap humanoid creatures, and Azura’s Star is only supposed to trap non-humanoids.
The major difference however is that The Black Star is currently bugged and will trap any soul for all creatures, including non-humanoids. This makes The Black Star immensely better than Azura’s Star, at least until it is patched (which may be a while since it’s not exactly game breaking).
Personally though, even without the bug, I would prefer The Black Star since there is an abundance of humanoids in the game, and any human trapped in The Black Star regardless of level is an automatic Grand Soul Gem.
To get The Black Star or Azura’s Star, you need to start the quest called The Black Star. Speak to Araneas at the Shrine of Azura, which is in the mountains directly south of Winterhold. Once the quest is complete, you will have the choice to return the broken Azura’s Star to Araneas or to a man named Nelacar in Winterhold. Returning it to Araneas yields Azura’s Star, and returning it to Nelacar will yield The Black Star.