Are there exceptionally rare items in Diablo 3 like the high runes in Diablo 2?

At this time there exists 5 amulets that are considered extremely rare. The drop rates on these are extremely low. The Star of Azkaranth having the lowest drop rate of every item in the game.

Source:

During the RoS playtest stream that occured on Tuesday February 18th, Travis Day stated that The Star of Azkaranth will be the rarest drop in Reaper of Souls. The reason for its rareness is because so many enemies use fire attacks in the game, which means that this amulet is the most usefull and most desired of the "Prevent all element damage" amulets.

• Talisman of Aranoch

• Countess Julias Cameo

• Maras Kaleidoscope

• The Star of Azkaranth

• Xephirian Amulet

Current Patch 2.0.5.

The closest items in similarity would be the Radiant Star gems.

The difference becomes that these items must be crafted, unlike say a Zod rune which had a very very small chance of appearing on the highest end opponents.

The similarity is that you need to use a large amount of lesser gems to create these gems very much like creating a Zod from lesser runes.