1. Class
2. Unique
Boss
Other chances at uniques
Iconic Mythics
The 13 pre-3.0 Mythics, now a separate track from Mythic-quality Uniques. Every lair boss can drop one, so you never waste a run, and Blizzard has stated Belial, Lord of Lies has the best odds.
Boss Trophies → Horadric Cube
Lair boss hoards drop Boss Trophies. Cube one to craft a dedicated unique from that boss — and there's a small chance it comes out Mythic. Crafted items carry the Crafted tag.
The General Unique Pool also rides along on every lair boss kill, though since Lord of Hatred it is a much smaller slice of boss loot. Each item's own card says whether it is in that pool.