1.) Static health bars. A character should have the same amount of health throughout the game, or grow only a little in HP. I like games where health slowly regenerates with time, too.
2.) Like in Clock's example of Megaman, equipment dependency, but without dependency on things like currency and shops. The best way to do this is to stop with random drops. If you fell a tough enemy, you should be able to strip his armor and weapons to make yourself tougher. Things that are evidently there should always be up for grabs. This would also allow for open-ended gameplay as players can confront challenges as they deem fit.
3.) A stat system that relates statistical growth to practice. For example, if you counter and parry a lot of blows, your DEX and AGL stat should increase. If you are constantly wielding heavy weapons in battle, or using vicious attacks, your STR should increase. If you block a lot, your DEF should increase. Though this does not solve the problem of farming stats (which is okay, because everything takes SOME extent of practice, even in reality), it does bridge the disconnect between skill and growth. When you finally get that stat up, you feel like it is because your character actually grew as a warrior.
4.) A similar skill system where your ability to perform battle techniques grows with usage, like in Tales. When you first learn a skill, it is rarely successful nor does it do a lot of damage. I would assume you are just imitating it. As you use the skill more often, practice and refine it, it becomes stronger and stronger. Eventually, you master it.
5.) Find a way to "learn" about your enemies. I liked how, in System Shock 2, you could pick up samples from fallen enemies, research them and learn how to better combat them. Often times, "weaknesses" boil down to exploitable attack patterns, elemental affinities or just plain being statistically weaker. Instead, there should be a "learning process" where you have to unlock the ability to exploit specific weaknesses either by researching it or simply through experience. For example, if you've never heard of Achilles and you fight him for the first time, how do you know his ankle is his weak point? You don't. You either need to read it somewhere or fight him dozens of times before you finally realize it. That should be the case with "weaknesses" for most enemies. If an enemy is weak to headshots, your character should have to fight maybe a dozen of them and then unlock a skill where now, instead of normal parries, if you parry against that particular enemy maybe you riposte by stabbing them in the head for extra damage. Stuff like that.