An Ultra Rare card is identified by having a gold card name and a holofoil image. The odds of getting an Ultra Rare in a Booster Pack was around 1:12 in Booster Packs before Soul of the Duelist. From Soul of the Duelist onwards, the odds became around 1:24. Reprint sets released after Soul of the Duelist such as Dark Revelation Volume 3 use the 1:12 ratio. After Tactical Evolution the odds dropped back down to 1:12. In the oldest OCG packs, such as Premium Pack 1 (OCG-JP), almost all cards are Ultra Rare.
In all pre-made decks, both starter and structure, there is one card printed in Ultra Rare. This is usually the featured card of the deck and the highlight of its collection. However, these cards are always predetermined, so it's entirely for show.
The chance of getting Ultra Rare cards in Duelist Packs is 1:12.
Ultra Rare cards are often more valuable than other cards, because they are harder to find and usually more powerful.
See also: "List of Ultra Rare Cards"