@Main Event - Those are all quest rewards from Daedric Princes - it's expected of them. I'll give you the masks though; but when most people mean unique loot they mean items you find and stumble upon. It doesn't have to be all-powerful; finding a Daedric cuirass perched on a near-missable alcove is just as unique as finding Mentor's Ring on a Draugr. It's the thrill of exploration, like in Morrowind - remember finding Mentor's ring in that seaside tomb? Or plundering an ancient archmage's vault? Or doing some throw-away quest and expecting some cash in return only to get a unique Daedric Dagger. To a lesser extent, it was also there in Oblivion; like the Dark Brotherhood's unique quest rewards for fulfilling a bonus, or stumbling into learning Finger of the Mountain from a Mages' Guild quest, or stumbling on to the Mundane Ring. Or even discovering Calliban's Retort or the Circlet of Omnipotence.
THIS ^
Azura's/Black Star, Dawnbreaker, Ebony Sword, Ebony Mail, Sanguine Rose, Mehrunes Dagger, and the list only gets bigger and better. There's also that unique Dragon Priest mask.
Oh my I forgot! It was so HARD to get them!
Most of the items You mentioned can be acquired so easily and/or replaced by something better. Just because they might have rare skin or name doesn't make those items truly unique. Skyrim item system made once really rare items/artifacts - not so special anymore. They might just look cool. My problem here is that with each next game there are less and less items that You really need to work hard to get. And it's not just that. It's the lack of Journal, magic Quest Arrows, too bright dungeons and caves that break the immersion.
To make it easier to understand. I once hunted for Daedric, Dwarven, Glass items.
Now I sell them.Unique - without an equal or equivalent; unparalleled.