I looked at this thread, the past couple of pages and my heart sank as I thought "Here we go again, have to try and explain it all once more," and realised that I just could not be bothered to write out an essay. So I went out into the garden and smoked my pipe (Coffee & Caramel flavoured tobacco - very nice, very smooth) and realised that without having to write an essay, talk about different weapons, armours and contexts and so on and so forth, I could sum up a melee in one paragraph (bear with me on this one - if it doesn't make sense then... well, my fault);
Have you ever stood in a big crowd? A big crowd of hundreds, if not thousands or tens of thousands? If not then I'll try to explain from my own experiences from two occasions that stuck in my head - both when I saw bands (MUSE at Wembley Stadium & Iron Maiden at Twickenham Stadium). You're there with people either side of you at the start, in front and behind, with enough space to comfortably move around a bit, move your arms, your own personal space. Then the band appears on the stage. Everyone in the crowd, except those at the front, moves forward to better see the band. Suddenly that personal space is gone as people press into you from behind, from the sides, you can't move properly as the weight of the crowd is pushing you forward, to the left or to the right. Those at the front resist and, like a tide, the pressure suddenly reverses, and then those at the back push forward again and it becomes a tug-of-war as the crowd pushes backwards and forwards.
That is what a melee is. Masses of people pushing forward, left, right, backwards, crushing you from all sides and even, as happened to me when I saw MUSE, lifting you off of the ground with how dense and tightly packed it is. Now imagine that the people pushing backwards are the enemy and they can't move properly as you can't - what would you rather have? A shield to passively defend you from the enemy, and to help use for leverage against them when it comes to the 'pushing match' or a second weapon you can do damn all with? At least with a two handed weapon such as a war hammer you can use it as a quarter-stave to push against your foes with or jab past the heads of your front rank to attack the faces of enemy who can't properly defend themselves. It's a no-brainer really - stay alive longer or die quicker.
Rebel King said:
this argument could apply for two handed weapons since it's an even better prey for archers since you would be slower and it takes forever to swing.
Swords aren't that heavy, I mean 5 pounds for each hand is nothing and I'm pretty sure even lighter for the main hero in the game.
Odds are if you're not taking a shield at all but carrying a two-handed weapon into battle at all then you're going to be wearing armour that is pretty much proof against missile weapons - that's why we see shields fading away with the rise of the plate harness during c14 onwards. Obviously a set of armour that may refuse even crossbow quarrels is going to be pretty damned good against melee weapons, so you're going to need something more powerful to defeat - hence carrying a two-handed weapon.
Weapons & armour are like computer virus's (weapons) & anti-virus software (armour). Let's say there's a new virus which defeats the best anti-virus software. The people who design the anti-virus software will go away and redesign/rebuild it until it will stop that virus. At which point the people who make virus's will do the same - go away and find a means to get past the ant-virus software (not the best analogy I know but it serves its purpose). It's an eternal battle of 'one-up-manship'.
As for two-handed weapons being slow? Weapons & armour are designed around being efficient in all aspects of their use and a big, slow, heavy two-handed weapon will not be carried into battle as it will most likely get it's wielder killed due to its inefficiency.
I'd advise stepping away from popular media and look into how weapons & armour actually work.
EDIT: Also, shields are awesome. They're not just for use against missile weapons - they're for use in melee for active & passive defence and as a weapon in their own right - you can use the rim against opponents and thump them with the shield's boss.