A man after my own heart. Shivs are the best! Other favorites of mine include Windshear (sorry, I know it's absurdly OP but it's also absurdly fun in a support role), Ebony Blade (endless combat, awesome aesthetic, and you can pick it up at level 20, what's not to love?), and Auriel's Bow (cool appearance, awesome effects).
Lately I've also been really loving the Bound Sword. I wish it had a simpler aesthetic, like the Blades Sword, but I love using potions and enchants to counter its inherent weakness of not being temperable.
And I love Silver Greatswords purely for their appearance. Throw on a custom enchant and they can wreak havoc at any level to boot.
Just a quick little tid-bit, if you're playing on a PC there is a mod out there (the name escapes me) that transforms all of the Skyforged weapons to look unique from ordinary steel weapons.
Of course it also aloows things like making the Skyforge weapons out of other materials like Dwarven and Ebony which may be a little "unreal" for some people.
Nightengale Sword or The Champion's Cudgel.
For non special weapons. The Glass Sword (Absorb health + Paralyze for one sec or Absorb Stamina) The Ebony Great sword. Whatever Smith, forged these weapons. May they enjoy everlasting glory in the many lines and numbers that they exist within.
I rather like there look cause I always go for a Ranger look like strider. The steel sword is the most carried and I would think that If there were actually rangers like that in skyrim they would carry regular swords not legendary or anything like that lol sorry I am a big Lord Of The Rings fan.
Stalhrim Warhammer with Frost Damage is probably the coolest weapon I've ever bought from a shop; amazing damage, good reach, and the simplicity of the design somehow makes it more appealing than the more detailed weapons.
My favorite unique weapon would have to be Dawnbreaker, because of the design of the weapon and also the effect it has on undead.