I definately understand that there are cards that allow your opponent to see what card you are choosing to be fair and honest. These cards do not have text stating the opponent must see the card, it is just a courtesy to make sure the opponent knows you are honoring your effects.

What I need to know is when it's not required for an opponent to know what card you are choosing.

For example:

#1
I play "Spear Cretin" in face-down defence and my opponent attacks it.
When the effect is triggered, must I show my opponent which monster I wish to special summon from my graveyard to my side of the field in face-down defence?

#2
I play "Magician of Faith" in face-down defence and my opponent attacks it.
When the effect is triggered, must I show my opponent which spell I wish to return to my hand?

#3
I play "Aprentice Magician" in face-down defence and my opponent attacks it.
When the effect is triggered, must I show my opponent which level 2 or lower Spellcaster I wish to special summon from my deck to my side of the field in face-down defence?

I know it's been a while since I've been here but don't hesitate to tell it like it is.

In all instances you have posted, you must verify to your opponent which card you are choosing.

The only time you are not obligated to show which card it is is when the card says "choose a/any card . . ." like with Different Dimension Capsule. Any other time that a card makes reference to a particular TYPE of card you must show your opponent to verify that the card you choose is the correct type.

Like Magus said, Different Dimension Capsule is one of few instances where you do not show your opponent what card you selected.

Usually, the only other times you do not need to show the opponent things is if it specifically says that you do not have to.

Other than that, anything let's you take things from your Deck, Graveyard or Removed From Play Area you must show to your opponent to verify that what you've taken is something legal to take.