GIFT BOX

One can find a Gift Box by killing Griswold in Tristram on Hatred difficulty. You may do so as many times as you want.

Gift Box
Gift Box
Put in the Horadric Cube and click Transmute!
Enjoy your gifts!

As the description says, you can cube it to get some items.

Gift Box → 3 different Regular Unique items (based on Character Class)

It always gives the same predefined unique item classes, depending on your Character Class.

AssassinAssassin WeaponAssasin ShieldBody Armor
AmazonAmazon WeaponAmazon HelmGloves
BarbarianBarbarian Class ItemSwordBelt
DruidDruid Weapon
or Other Weapon		Druid HelmBoots
NecromancerNecromancer WeaponBody ArmorHelm
PaladinPaladin WeaponPaladin ShieldPaladin Helm
SorceressSorceress Weapon
or Staff		Sorceress ArmorStaff

NOTE: These Uniques cannot be disenchanted at Tier 1, but can be disenchanted after uptiering them.

SPECIAL BOX

One can find a Special Box by killing Griswold in Tristram on Terror difficulty. You may do so as many times as you want.

Special Box
Special Box
Cube with an Oil and click Transmute!
Enjoy your gifts!

As the description says, to get some items, you can cube it with any of the 6 Oils available at weapon shops.
Note that some outcomes are more likely than other.

Special Box + Oil of Renewal → (1 to 3) Arcane Shards or (1 or 3) Arcane Crystals
Special Box + Oil of Enchantment → 1 to 3 Signets of Learning
Special Box + Oil of Craft → 1 to 3 Shrines (random)
Special Box + Oil of Disjunction → 1 to 3 high level runes
Special Box + Oil of Absolution → Set item* or Apple
Special Box + Oil of Luck → Blessed Oil of Luck**

* One specific item from each set can never appear. Testament of the Apes, Yshari and Tribute set items can never appear.
The item will have just 1 socket, and cannot be disenchanted to Arcane Shards.
** Check the following sub-section for a detailed explanation.

BLESSED LUCKY BONUS

As the Lucky Bonus recipe, this one adds small bonuses to the items. There's a lower chance to gain the bonuses, but they are much better than the Lucky Bonus. Any item that has been transmuted with this recipe will show up as "Already upgraded!". Items marked as such cannot be used for this recipe.

Any item + Blessed Oil of Luck → returns item, may add bonuses

This recipe has 15% chance to add any of the following bonuses:

Weapon: +(40 to 60)% Enhanced Damage and/or (100 to 200)% Bonus to Attack Rating
Armour: +(40 to 60)% Enhanced Defense and/or Damage Reduced by (1 to 2)%
Amulet: +(1 to 2) to All Skills
Ring: +(10 to 15)% to Spell Damage
Quiver: (5 to 10)% Bonus to all Attributes
Jewel: +(2 to 4) to Strength and/or +(2 to 4) to Dexterity and/or +(2 to 4) to Energy and/or +(2 to 4) to Vitality

See THIS PAGE for more information about the Lucky Bonus.