Use Magic Device may be the most useful skill in Dungeons and Dragons. It allows for the use of items that require a certain trait without actually having that trait. For example, a Wand of Cure Light Wounds requires that the person to use it have the spell Cure Light Wounds on his class spell list. With Use Magic Device, a character can emulate that criteria, having Cure Light Wounds "appear" on his or her spell list, even if that character has no spell list in the first place. It also allows a character to use scrolls, staffs, or items that have an alignment requirement, such as the Holy Avenger. This in itself is extremely powerful, allowing Rogues and Bards access to a multitude of magical effects without relying on a Wizard/Sorcerer or Cleric/Druid for those effects. What Dungeons and Dragons party would not want an extra character to be able to cast healing spells or a Rogue to be able to cast his own "self-buffs" such as Invisibility or Haste?
Then there are the classes that have abilities based around the skill, such as both the Warlock (Complete Arcane) and the Artificer (Eberron Campaign Guide). Both of these classes gain the ability to roll Use Magic Device to gain access to the spells required to make items. The Warlock, at 12th level, is able to forgo having the spell available when making a magical item and instead roll a Use Magic Item check to emulate the spell for this purpose, allowing him to make any item in the game that he has the prerequisite feat for. The Artificer gets this ability at first level, and cannot use his own spells for this purpose at all. Instead, he must use the skill to emulate the spell desired, allowing him to make full use of his class, as he gets 75% of all magical item crafting feats built into his level progression, as well as a bonus "crafting pool" with which to pay for the experience cost of crafting magical items.