A hand is a resource in combat and to go into combat with the intention of deliberately forsaking some of your resources is stupid. The only fighting style I know of that only uses one hand is olympic style fencing which is a sport and not a true combat form. Granted olympic fencing descends from small sword combat but that was a ritualized dueling style. This is not to say that there is no valid option but to have a second weapon, or a shield.
Things to do with your off hand in DnD combat:
Punch someone, works better if you have a monk level, or some feat investment.
Grapple someone, as above.
Throw/Catch an item.
Grab the McGuffin of Doom.
Hold/use a potion.
Hold/Use a wand or other magic item.
Hold a ranged weapon like a throwing knife or hand crossbow.
Open a door.
Throw the switch.
Throw the halfling.
Hold a light source.
Make gestures.
Cast a spell. (Only takes one hand.)
Things which can be done in reality but are modeled poorly in DnD:
Armour your hand and use it to parry with. This is my favored (SCA fencing) fighting style and is quite effective, though more so against rapiers than, say, axes.
Use a hard parry object, like a stick. (How Thorin Oakenshield got his name.)
Use a soft parry object like a rope or cloak. I personally love this style, lots of options.
Note that while DnD models these things poorly by default, it's pretty easy to set up house rules or feat chains to support them.
Personally if I was going to make a character who like to have the option of doing something with his off hand, but doesn't want to penalize himself I'd wield a medium sized weapon like a longsword two handed so I can always free up my off hand with a free action. If you have a feat to spare the bastard sword is the ideal choice here.
