The majority of true rares traded on this forum came from the following sources:
Server Birth - In the early days of UO certain items around in cities that were decorating towns like Britain could be stolen right off the tables or floor they sat on. Some people hunted down these items when they were available (about 9 years ago). After the Trammel/Felucca split, the stolen decorations were all restored to the cities in a new unstealable form, but those already stolen were still in the hands of players. This is the source of most the rare but seemingly household items, like playing cards, ceramic mugs, and spittoons.
Expansion items - When new lands were added to the game, sometimes a certain portion of the decorations on the new land would be stealable the same as the original server birth items. This is the source for things like magic doors, lights, and certain other items from Khaldun dungeon, for instance.
Seer items - Years ago there was a program where volunteer staff working for UO would make quests for players to participate in. Sometimes the Seers in charge of these events would be able to give away special rewards to participants, or people obtained items due to accidents (like a seer character dying and being looted). Usually they were uniquely hued and named items. Most of the weapons and armor obtained from this time are rather weak because it was created before the Age of Shadows item system was implemented. The exception is the Seer-created Vine Cord Sandals.
EM Items - These are the most popularly traded items on this forum. They come from a later incarnation of the quest program, this time run by Event Moderators. These items range from uniquely hued decorations to incredibly powerful unique weapons. The Em Program ran for a number of seasons, and the items given out have been documented in a post stickied at the top of the forum. This program has been terminated.
Live Event - Currently all quests are handled on a game-wide automated system. Although this means there is a lack of the possibility of a specific Event Moderator giving away a unique item with personal character, it doesn't mean the end to rare items. Quests like the hunt for Ricardo the Thief allowed whoever first found the entrance to Ricardo's lair to obtain some very valuable rares that were Ricardo's treasures (Pilfered Painting, etc..) The most recent true rare creating event was the destruction of Magincia, which created rubble of the city structure and allowed players to take what they wished from the city. The event also added some specific new items such as Rift Pillars and daemon blood.
To obtain any of the rare items that came from the past events, a player either needs to buy them or hope to find items in the collapse of a former player's house. To collect any future rare items, a player would need to pay attention to what events are coming and be a clever participant.
As DVI also said, there are other items that originated from bugs. Sometimes bugged items have a dubious reputations due to the nature of the tricks that create them. The desirability of these items is dependent on the source of the item or the extent to which they were created.