Physical combat

Melee vs. ranged The choice between melee and ranged combat depends mostly on your class. Most classes have all their best abilities in one category. Some are lucky enough to have some abilities designed to help them switch to their preferred range, such as Wing Clip. Below are tactics for keeping your foe at your preferred range (especially when it is not theirs).

Dual wielding Your total damage output when fighting with two weapons should be higher than fighting with one weapon and a shield, but roughly equal to fighting with a two-handed weapon. Off-hand weapon attacks deal 50% of the weapon's designated damage. Therefore, it's wise to always put the best "damage dealer" weapon in the main hand. Dual wielding also increases your base miss chance using the formula 80% × M + 20% where M is your miss chance when not dual-wielding. Your usual miss chance against an opponent of equal level is 5% which means the typical miss chance while dual-wielding is 24%.

A Rogue with the dual-wield talent increases the off-hand weapon's damage from 50% up to 75%. They must also have 5 points in Precision, which increases chance to hit by 5%.

A Fury-talented Warrior with the dual-wield talent increases the off-hand weapon's damage from 50% up to 62.5%.

Dual wielding versus two-handed weapons First a note:
Rogues are not included in this because they are built around dual wielding. They have no ability to use 2 handed weapons.
Also not included are sword and shield. That setup is for defense and will never compete for DPS.
For both those situations, you would have the same weapon versus the same weapon x2 and since the miss rate and offhand damage reduction do not equal 100% reduction (if they did, no one would ever dual wield) debating the dps merits would be pointless.
Druids are a special situation. When shape shifted they do not derive ANY dps from their weapons and cannot choose to dual wield or not.

About each class:
Warrior:
DW talents:
Dual wield specialization: 25% increase to offhand damage
2 Hand talents:
Two Handed Weapon Specialization: 5% increase to 2 handed weapon damage
Both:
Precision: +3% to hit (This affects both and it is possible to get it with either talent spec, but is more likely in a DW build, so we'll ignore it.)
Sword/Poleaxe Specialization: +5% Crit/+5% chance extra hit (This also affects both talent specs, but is more likely in a 2 hand, so we'll ignore it)

Shaman:
DW talents:
Dual Wield Specialization: +6% to hit when dual wielding
No 2 handed talents.
Both:
Nature's Guidance: +3% to hit

The talents are pretty much a dead give away as to the viability of DW or 2 handed for Shamans, but we'll run the math anyway. (Also note the shaman abilities are weighted toward dual wielding. Stormstrike is unnormalized and hits with both weapons. Shamanistic Rage gives mana on hit and is not based on weapon damage.)

Some Basic DPS Math:

Assume two 1H weapons, each delivering x DPS
Assume one 2H weapon with y DPS
All classes capable of dual wielding without any applicable dual-wield specialization
1.5x × (1 - 0.24) = 1.14x
Warriors with top-rank dual-wield Specialization
1.625x × (1 - 0.24) = 1.235x
Shamans with top-rank dual-wield Specialization
1.5x × (1 - 0.18) = 1.23x
2H weapon for Shaman or Warrior without talent
y × (1 - 0.05) = 0.95y
2H weapon for Warrior with talent
1.05y × (1 - 0.05) = 0.9975y
+ Section below not yet modified +

For weapons of equal dps, x will be approximately .76y.

We know from these equations then, that:

Dual-wielding classes not dual-wield-talented have their DPS increased by 20% when wielding two weapons with the same DPS. (1.14 / 0.95 = 1.2)
Warriors with top-rank dual wield talent have their DPS increased by 30% when wielding two weapons with the same DPS. (1.235 / 0.95 = 1.3)
Two-hand or sword-and-board warriors have their DPS reduced by 5%, unless modified by talents and +hit gear.
Shamans with top-rank dual-wield talent have their DPS increased by 30% when wielding two weapons with the same DPS. (1.23 / 0.95 = 1.3)
In order to determine which weapon combination is superior, then we equate the two formulas:

For non-dual wield specialization warriors
0.95y = 1.14x
Which then reduces to
y = 1.2x
This tells us then that a two-handed sword must at least have about 20% more DPS than each of the two individual swords.

This also means that dual wielding receives 1.2 times the damage bonus from attack power. This is because power affects both main- and off-hand. Thus with enough power, dual wielding will always be better than using a two-hander. Imagine having a 80 DPS two-hander and two 10 DPS swords. But you have 5600 attack power.

Two-hand DPS becomes (using above formula): 0.95 × [80 + (5600 / 14)] = 0.95 × 480 = 456

Dual-wield DPS becomes: 1.14 × [10 + (5600 / 14)] = 467.4

The level 15 white one handed swords do more DPS than the hardcore raid epic two-hander!

This is of course a rather irrational example as it is impossible to attain 5600 power, but it illustrates that attack power scales better with dual wielding.

For dual wield specialization warriors
0.95y = 1.235x
Which then reduces to
y = 1.3x
This tells us then that a two-handed sword must at least have about 30% more DPS than the DPS of each of the two individual swords. And that the dual wielder receives 30% more bonus from attack power.

Examples seen in weapons
Taking a look on Thottbot to see what 1H and 2H "green"-quality swords there are around level 30-35 will give us the Nobles Brand set of 1H swords (22.1 DPS, level 35) and the Frost Tiger Blade (28.8 DPS, level 35). The 2H blade's DPS is about 30% more than the 1H blade. Another example would be the 1H Jade Serpentblade (18.3 DPS, level 30) vs 2H Stonecutter at (23.9 DPS, level 30). The 2H blade's DPS here is again 30% more than the 1H blade.

We can then conclude that unless you are a Fury Warrior with dual wield specialization, the better weapon choice to increase DPS is to use a two-handed blade. Even with dual wield specialization, a two-hand weapon is equal to two one-handed weapons of the same quality. However, the extra rage generation given by the tier 2 warrior talent Unbridled Wrath tips the balance in favor of dual wielding for fury warriors that take both talents.

Dual-Wield benefit Conclusions
If your 2H weapon shows more than 20% (for non-dual wield builds) or 30% (for dual wield specialization builds) extra DPS than your 1H weapons, and you don't have Unbridled Wrath (for Warriors), you're better off using that.
keep in mind that you also receive 20% (or 30% for the spec builds) bonus to the DPS from attack power while dual wielding. It's up to you to decide if your attack power is high enough to bridge the quite probable gap with 2H DPS.
Basic dual wield gives a 20% DPS increase over using a one-hand weapon and shield.
It also gives you a 20% bonus to the DPS gained from attack power.
Warriors and Shamans with Dual-Wield Specialization get an additional 30% increase on their base DPS (or 10% on top of the basic dual-wield DPS without talents).
Rogues with Dual-Wield Specialization get an additional 50% increase on their base DPS (or 30% on top of the basic dual-wield DPS without talents).
These same percentages apply to the DPS bonus from attack power.