Two-handed weapons cannot be used in conjunction with a shield. All Weapons, save for Wands and Rods, have their own two-handed weapons.
There are currently no non-weapon items that require two hands.
While all two-handed swords can only be wielded by knights, some (but not all) two-handed clubs and axes can be wielded by other vocations as well.
Advantages and Disadvantages
Advantages
Two-handed swords are useful when increasing the hunting speed since they do a lot more damage than most one-handed weapons.
Disadvantages
While wielding a two-handed weapon, the player suffers more damage from monsters since no shield can be equipped and hence, the shielding skill does not increase.