At first glance, it can seem like the question to ask yourself when designing a combat system is "How can we have everyone kill each other?" This is certainly an important question, but I think the real question is quite the reverse. That is, "How can we keep people from killing each other?"
Why? Ok, consider most any other action in an RPG or story. You want to lift a rock? Maybe roll some dice and you lift the rock. Ditto for climbing a rope, charming a barmaid or anything else. But when the action is "Stick my sword in that guy" we're uncomfortable with it being that straightforward, and when it comes to the other guy trying to stick his sword in us, then we definitely don't want it to be that simple.
So with that in mind, the real purpose of the combat system is to make the process of killing someone take enough time and effort to complicate matters without making things un-fun. That is, I admit, a kind of callous and disturbing take on it, but the role of violence in RPGs is a bit of a messy topic (and one I'm not really going to drill into at the moment).
On the "not making thing un-fun" front, many systems put a subtle (or not-so-subtle) thumb on the scales in support of the idea that the PCs are going to win any fight they engage in, albeit at some cost. This is a tricky balancing act because we instinctively want a "Fair fight" but we also want a fight we can win. This is the sports movie paradox, and it pops its head up in RPG design in a lot of odd places. This is a big issue, but it's also a high level one, which makes it hard to address at this point.
In terms of complicating violence, the trick is that the heart of a combat system is not dealing damage, it's damage mitigation. Not that dealing damage in unimportant, but rather it's simple and straightforward, and if that's all there was to it, then combat would just be back to the straightforward "I put my sword in his gut". Mitigation is all the reasons that you can't put your sword in his gut, or that it doesn't end the fight when you do.
Classically, this divides into two things - defense and resistance - though that is a division born out of tradition more than necessity. Defense is all the reasons why something wouldn't hit you (that is to say, have no subsequent mechanical effect) while resistance is all the reasons that a hit doesn't end the fight (such as damage reduction or hit points). This sounds tidy, but historically it's very muddled. Consider the role of armor - is it a function of defense or resistance? You can make a case for both (and, indeed, in some systems it has elements of both) and in doing so you highlight the division.
There's a reason that this model lines up with a similar two-part model for offense - roll to attack + roll to damage. They're opposite sides of the same coin, and a lot of games have streamlined both of these things into a single roll to hit, with damage based on Margin of Success plus some modifier (such as weapon or strength). This is certainly easy, but it tends to encounter predictable problems. Specifically, it tends to make whatever stat covers accuracy into a super-stat, and it does weird things when dealing with weapons at extremes of the damage range (since it can make "0 damage" weapons, like a ping pong ball, lethal).
Unfortunately, the alternate approach of adding more layers of rolls (say, one for attack, one for penetration and one for damage) gets cumbersome quickly, so it's not a solution either. Practically speaking, we're limited to a small number of rolls for an exchange in combat, but at the same time we want it to be more than just a single exchange. So where does this leave us?
Well, let's look at what we have for dice. Right now, our core idea is that a normal success is easy to achieve, and there's not much that's more normal than whacking someone. This means we've got a default assumption that it's pretty easy to hit someone, and I'm ok with that, because it is. And that, right there, speaks to something of a design goal - the purpose of every swing in a fight is to end the fight, so there needs to be a good reason it doesn't.
Having a goal like that is essential to making a combat system do something other than emulate another combat system you're familiar with. That specific idea is a somewhat brutal design goal, and it won't stand on its own, but it's a great start, and it gives us something to build from for the next time.