I carry an ebony dagger and my nightingale blade when I dual wield. One for stealth kills, the other for combat.
I generally like to carry two war axes. One of the best for me, but if I had to use any other, it would be a Sword and a Dagger.
Bound Swords, because they are very good Weapons from beginning to Mid game, and they are wieghtless. If My character decides to use Elemental Fury, then I prefer an unenchanted Dagger in the offhand, and a powerful Enchanted Weapon in the Right Hand. I have a preference for Ebony Axes that are Enchanted as Main Weapons for My characters when they are at higher levels.
The "ideal" combination for overall damage is a Mace in the Right Hand, and a Dagger in the left.
I use sword mainhand(the armor ignore from maces isnt enough damage to beat the visuals of swords for me), and dagger offhand. I like rocking that duelist style, and having a fast weapon in your offhand makes your main swing faster.
Does anyone know if daggers that have been smithed up to legendary benefit from one-handed damage enchants? It says on UESP that they dont, which is lame.
I rock two daggers when dual wielding, as I only dual wield as an assassin. Sometimes I use 2 Daedric Daggers, but mostly I go with Mehrunes Razor on main hand and Blade of Woe on offhand. Pretty damn great if you ask me xD
My assassins/thieves usually duel wield in close quarter combat. My weapon type of choice is duel daggers, just for the pure speed.
I use my custom Chaos Dadric Sword in my main hand, and Dawnbreaker in my off hand.
My one dual-wielding character uses two elven war-axes named Flesh-burner (25 hp fire damage) and Blood-drinker (13 hp health absorb). I can't really get into swords or maces as much.