Beside my alltime favorite the Skyforge Steel Greatsword, I go for the Ebony Blade which my char use with several of her outfits. She was able to change it a bit against those cannibals during "The Taste of Death"
Excluding self-enchated ones, my favorites are:
-Chillrend. 25% chance to paralyse + cold damage. The highes level version has the same base damage as Dragonbone sword, and it also benefits from perk (Glass). And it look very cool.
-Skyforge weapons, as you need only the Steel perk to improve them, however they are as strong as elven weapons, they are even lighter. They look great too.
-Blade of Woe. Highest base damage dagger, requires only Steel perk to improve and it look cool.
-Staff of Chain Lightning. It has a stagger effect as destruction spells have when dual cast.
-Wabbajack. It is sooo funny. Not to mention Henson's new research which says that it is not influenced by game difficuly.
The Nightingale Blade is my personal favourite. I love how it's so sleek and elegant, and the enchantment just means you can keep on sweeping and slicing. Auri-El's bow is my favourite bow as far as design goes.
Other weapons I like are the Dwarven Dagger, it's nice and big and angular. Elven swords, daggers and bows, Nordic Swords, Blades Swords, Dragonbone Daggers and probably Glass weapons too.
I like the realistic look of the silver weapons. And mostly all of the realistic looking styles like iron and steel. Although I never use it, I love the eagle head of the Elven warhammer. The glass waraxe has a cool symmetrical look. I like the brown colored bows: long, hunting, and imperial.
Mehrune's Razor is the best dagger all around. Volendrung is amazing for a fantastical, Thor-like character. Seriously, "The Rock" couldn't swing something that size like that. Sanguine Rose is a beautiful staff to wield. Right next to the Staff of Magnus in terms of looks. I don't much like the awkward lines of the Daedric and Nordic weapons. Stalhrim is pretty comical and fantastical. Scimitars are amazing. As well as the "Blades Swords"... AKA katanas.