I've played many games throughout the years, and have found that all the systems are based on one mechanic. Roll and beat a number.
You roll your attack dice, the defender rolls his defense dice. If attack wins then you apply damage. Sometimes these systems simplify the opposed roll to just "roll and beat the target number" - d20 is the obvious example.
Some of these give you the option of choosing to defend or not.
Example Games With Counter Roll: White Wolf Systems (Vampire, Werewolf..), Deadlands (original not d20), Brave New World, Feng Shui
Example Games With Roll Against Defence: d20 anything
Now to get into some specific details ...
ACTIONS (and INITIATIVE)
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Some systems allow multiple actions in the combat round based on your abilities, or powers, or perhaps some form of quickness determination.
d20: uses your level to decide number of attacks (everyone has the same number of actions though), and a d20 roll for intitiative. You have no real "defense" option except by using feats and/or full defensive action.
White Wolf: everyone has one action per round but may "split" this action into multiple actions by sacrificing "dice pool". Essentially you reduce your chances of success in every thing you wish to do, the more you want to do. Certain powers/abilities allow you to gain more actions beyond the first. The obvious one is Celerity in their Vampire System. Initiative is based on a roll as well. An action may be used at any time to perform an active dodge. This gives you a chance to roll against the attack roll.
Deadlands: you roll against your quickness. Your result dictates how many actions you get. These actions are represented by drawing cards from a deck. Highest goes first, then the next highest etc ... until you have no cards left. You may sacrifice any action to actively defend.
DAMAGE
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Many systems have many types of damage resolution. Most of them rely on damage dice, however some simply use target numbers to apply 1 unit of damage.
d20: you roll damage dice and remove from a hit point total
White Wolf: you roll a number of dice for the weapon and each success is a wound level. The opponent always gets to counter this with a stamina roll. The left overs are applied to wounds.
Deadlands/Brave New World: you roll damage dice against a target number and this determines the number of wounds taken to your hit points. You also detemine the location of the hit as well.
ARMOUR
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Systems generally use armour in a couple of ways.
1) it increases the difficulty to hit you
2) it reduces the amount of damage you take in the end
3) it increases the "soak roll"
d20: increases difficult
Tunnels and Trolls: reduces the amount of damage you take
White Wolf: increases the dice you roll to soak damage
I think that should get you started.