In my (admittedly not huge) DM experience, I've seen a number of rules that are either contested, or not fully understanded by other players.

Here I'm going to talk about probably the most common gripe I've heard... and that's AC (or armor class).

AC is basically a measure of how hard you are to hit when someone attacks you.
Basically - for anyone not in the know - since 3rd edition, AC is a number which an attacker has to match or exceed with an attack roll in order to score a hit; the larger the number, the harder it is to do this.

AC is made up of several factors; a standard 10 base number, size modifier (the bigger they are, the harder they are to hit), natural AC (due to thick scales, hide etc), Dex AC (how well you can duck and weave out of harm's way), Armor AC (due to the specific armour you're wearing, Shield AC (due to any shield you're carrying), and various AC bonuses from magical sources (Deflection, Divine etc).
Sum this all up, and you get your overall AC.

Now here's the controversy:
Some people claim that wearing amour shouldn't give you a boost to your AC, but rather should grant the wearer damage resistance (reducing the amount of damage you take from a sucessful hit).

Now, other than being difficult to implement due to balancing issues (as I've heard from game designers), this is a completely unecessary idea based on incomplete understanding of the mechanics of the game.
The normal AC system is also -in my opinion- far more realistic than the alternative.

This is the misunderstanding as I see it:
When someone fails to make an AC with their attack roll, most people see this as a 'miss':
You've swung your sword and the monster ducked completely under it.

Now, in some cases this is correct... if you roll terribly for attack, you can miss outright, and if your opponent has high Dex but light armour this is also likely to be the case.

At this point, a DR-pusher might say:
"But armour should cause the wearer difficulty in moving, rather than making them harder to miss... by removing the AC bonus, and replacing it with damage resistance"

Again, this is wrong. There is already a system to slow armour wearers down significantly... the Max Dex limit for the armour. Basically, if you're wearing full platemail, the most your Dexerity (and thus your Dex AC) can be is +1. For Leather armour, this is a much more reasonable maximum of +6, meaning that you can duck and weave quite effectively, but unfortunately, you have much worse protection.

So lets look at what AC really means:
AC is a measure of how hard you are to hit, as I already said. The key point to take in though, is not that not making the AC with an attack means you fail to hit your opponent; it means you fail to score a hit that damages your opponent.

Let's look again at the case of full plate armour. Say you made an attack on the warrior in his full plate, and you manage to beat his AC.
You swing your sword valiantly and- ...then what? Do you smack his breastplate with your blade and watch as somehow the slash cuts him inside his armor? Does your blade cut through the steel altogether?

Of course not... that would be silly. What happens is you strike a vulnerable area with your sword... the joints in the steel, or the places where there is less protection.

Let's do a recap. This was in one of the core rulebooks (I forget which one), in an often forgotten section.
What does your attack roll mean?

If your attack roll is less than 10 + your opponent's size modifier, then you missed him completely. He didn't even have to dodge, you were miles out.
If you roll slightly higher than before, but still less than 10 + size + Dex AC, then your foe has nicely dodged your attack.
If your roll exceeds this, but not by enough to overcome the shield bonus as well, then your weapon was deflected away my your foe's shield.
More than the above, but less than his magical AC bonus(es), then your blow was deflected away by an invisible, magical layer of force.
Higher still, but not above your enemy's armor bonus, then CLANG you just smacked his armor, but didn't score a hit.

If after all that, you beat his overall AC altogether you have made an attack that scores a hit in the gaps of his armour, and have wounded him.

All in all, that's a fairly comprehensive system that fully captures actual battle, wouldn't you think (excluding the magic, obviously)?
In the midst of a gaming session, it would really take to long to work out exactly what kind of miss an attack was, so it tends to default to "you missed", thus it's understandable why some people have gotten it into their heads that you miss altogether.

Ok, so now that I've defended the existing system for being completly valid and effective... let's see the alternative.

Damage resistance pops up in various different monsters. It's basically a way of saying that, a creature can take a hit, and not worry about damage from it.
Usually, damage resistance reduces any damage recieved by 5 or 10 points (though cases of greater damage resistance exists). Also, most damage resistance has a certain way of overcoming it.
Magic overcomes *all* damage resistance, but beyond that there are types that are overcome by magical weapons of certain strengths, some which are overcome by certain types of damage (zombies, for instance take normal damage from bludgeoning weapons, but not from slashing or piercing weapons since zombies aren't really using their organs anyway... who cares if you poke a few holes in them?) and some which require a specific material that a weapon needs to be made from in order to overcome it (lycanthropes are a big example here... everyone knows you need sliver weapons to harm a werewolf).
But regardless of the strength or what overcomes it; all damage resistance can be overcome if you do enough damage.

Let's think back to our poor friend trying to cut through his opponent's plate armour.... better yet, let's give him a dagger instead.
If the armour had damage resistance, rather than an AC bonus then if our friend was strong enough, he would be able to stab you quite easily through your steel armour.
That doesn't sound quite right, does it?

There are already rules in place that allow you to try and break your opponent's equipment, armour included... so let's not mess with the rules and make everything unbalanced and silly because of a misunderstanding, eh?

Note: I want to point out that I'm aware I alternated between 'armor' and 'armour' several times there.
This is because terms like 'armor bonus' are written that way, and I don't like messing with technical terms in case it causes confusion. Writing armour, as in the noun 'armour' however I am more than willing to do.