Below are a few combat systems I like, that have cropped up across numerous games.
The Roll Over System
The Roll Over system is used in every edition of D&D after second, Lamentations Of The Flame Princess, and every other damn d20 system game ever made.
In essence, a roll over system involves rolling a die and hoping for a high roll. In D&D, this is typically the d20, which you then apply a bunch of modifiers to and try to roll over your target's Armor Class. Its much more straightforward than the weird combat charts of the older editions.
- Easy to explain to new players
- Easily scaleable, simply make the target number higher
- A little difficult to determine probability of hitting
The Roll Under System
The Roll Under method of combat is used in The Black Hack, Basic Role Playing, and Warhammer Fantasy Roleplaying (I think).
There may be different dice involved, different numbers to roll under, but the core mechanic is the same: Roll a die, you want to roll low. Its simple, quick, and efficient. Typically the number you must roll under in order to hit is listed on your character sheet, rather than in D&D where you roll a d20, add a bunch of modifiers, and hope for the best. In d100 systems, this typically means you know your percent chance of hitting when you're going to attack.
- Easy to determine probability of hitting
- Target number is typically listed on Players' character sheets
- Discourages risk taking in my experience, as players with decent chances (50% or so) may not attack as they feel its not worth the risk
Opposed Roll System
Opposed Rolls are used in Tunnels & Trolls and Fighting Fantasy.
With an opposed roll combat system, both the attacker and the defender roll dice. In most systems, whoever rolls a higher value deals damage, though in some cases a defender rolling a higher value may simply mean they dodged the attack. This system adds a touch of variability to opponents, as its difficult to determine how easy they are to hit. This can be a good thing, as it adds chaos and randomness to combat, but it also makes it difficult to figure out the odds.
- Can add chaos and excitement to combat
- If fighting against more powerful opponents in systems where the winner deals damage, it can be very difficult to survive, as chances are that the defender will deal more damage than the attacker
- Very difficult to determine chance of hitting an opponent
"Screw it you do damage" System
There are only a couple systems that use this mechanic, including Maze Rats, Into The Odd, and a homebrew role playing game I wrote when I was like 11.
With this system, all attacks hit, always. Either characters have large numbers of hit points or hit points represent dodging attacks, with permanent damage being dealt to another attribute. Armor is typically represented by damage reduction of some kind. This system makes combat very quick, but it can also be quite deadly.
- Extremely simple
- Can be quite lethal (though this isn't necessarily a bad thing depending on the game)