1. The Divine Gift
The item was a reward provided by a divine/supernatural entity, made to be a worthy gift for the recipient. Myths and legends are rife with this origin. Excalibur for one.
After being plunged deep into the heart/crushing the head of an enemy, a lover, a liege, a family member, the weapon became invested with the slain person's spirit, or the taint of the crime.
3. A Singular Event
An item was used in some famous, pivotal act such as a battle, a unique feat of arms, some dreadful atrocity, etc. The collective awe of the populace has imbued it with power.
4. A Piece of Greatness
The item has gained its powers through association with some powerful entity, such as a Saint or Great Hero. Sometimes these are in fact body parts of said individual and properly termed relics. No effort was made to create the item, it has simply acquired these attributes by their association with the being.
5. Beyond Mastercraft
The item is of such legendary quality that they surpass the normal bounds of reality. The craftsman put such time, skill and energy into the item that the universe itself has gifted it with the power to bend reality in some way. The sublime Boots Too Fine For This earth by Captain Penguin are the epitome of these.
6. Lightning Strikes
Some massive discharge of energy - magical, mystical, diabolic, etc, resonated with the item in some manner and granted it power. Muro’s Gravediggers Legacy is an example of this one.
7. Lost Technology
The item was once part of the standard equipment of some long lost empire and was mass produced in its time. The ages have scattered and destroyed most specimens. This works especially well for items that can not be created easily in the current campaign world.
8. Special Ingredients
The item is created from a special magical material and all of its powers are drawn from this source. An example of this is the Soulturner of the Spring, created from the Shards of the Storm. A simpler example are the Gems_of_the_Underworld.
9. Magical Body Part
This item was once part of a magical creature and although separated from that creature, still retains powers associated with the creature and its body part. An example would be Medusa’s Head used by the Greek hero Perseus.
10. Divine Inspiration
The item is crafted by the hands of sentient beings, but inspired by divine help. This is an example of this, though the god or being that aided her is anonymous.
12. Sub Conscious Creation
Ah, the mysteries of the mind. Coupled with mysteries of magic, and you can get this.
13. Unexplained Discovery
A cop out, but it hints at mysteries. The item’s origin is lost to time - someone simply has found it in some odd location, or something that has been around has been found to have magic powers.
13. A Fine Pedigree
The items are magical because their creator was a entity infused with great magic, power and/or divine favor. i.e. http://strolen.com/viewing/Nial_Ironspirit
14. Merely a Shell
The item itself is not at all magic, but all of its powers derive from a being that either resides or has been trapped within. See The Band of the Revenant for details. Another excellent example is https://strolen.com/viewing/Glaive_of_Balundir
Additional Ideas (2)
The item just fell from the sky one day. Everyone assumes it was from the gods, but a close examination by a person of knowledge will reveal this is clearly a work of complex handicraft from some unknown being. Perhaps a passing UFO tossed it out with the trash.
The item is only magical because everyone thinks that it is, meaning that it has no effect on those from another culture.