Hmmm.. I've definitely seen specific gems or uniques that only drop from certain elites or bosses. Some of them, it's something they always drop, but for others it's something you might or might not get.
As for cool enchantments, there's a pretty wide range. My favorite are probably "Augment" items. When you find them they have a few particular enchantments and something that says to kill like 50 Zombies/Spiders/Goblins/whatever, and when you finish doing that they gain a few extra enchants, often including chances of certain spell effects on hit, like 10% chace to cast Web, for the spider augment.
The simultaneous use of a 1-hand melee weapon and a 1-hand ranged weapon shall henceforth be known as "Swashbuckling";
It needed a really cool name to make up for the fact that nobody likes to do it.