1. Over time we have done away almost entirely with die-rolling, even for combat. (Most of us had enough combat experience to demonstrate properly, and those who don't can guide the others.)
Instead we use a system I call, and maybe others do too, describe and demonstrate, as much as is possible. Players describe what can be described and demonstrate what cannot be. In rare cases, like in certain combat situations, or by choice, the player can decide to use a die roll. For instance in a combat or save they may say, "I choose to roll the dice." If they do I allow it, but they must stick by that decision. If the die goes against them, they are stuck with that. But if they do not choose to roll then they can modify situations to the best of their ability to describe or demonstrate.
2. We use partial success and failure, rather than, "you succeeded entirely, or failed entirely."
For example say someone examines an object. Based on their description of what they are looking for, or by demonstration of how they go about it, they may notice some things, and not others. They of course may succeed entirely, or fail entirely as well, but it is not necessarily either/or.
3. I give out Experience Points based upon situational circumstances rather than by pre-arranged formula. If a troll is extremely easy to kill, or requires little creativity or cleverness, then they get few XPs for such a situation. If a bandit is extremely hard to kill, proves dangerous, or if they are able to capture, subdue and extract valuable intelligence from that individual, then I award more experience than I would for the troll, regardless of NPC or monster level or challenge rating. The difficulty of the actual situation faced is then paramount, not the abstract value of the encounter. I've done that forever it seems like. That may be the oldest variation I ever made to the game.
4. Player Skills - Real World skills and capabilities of the players are allowed to be utilized in-game and are actually written into the characters (within reason, certain real world skills of the players do not translate to a D&D milieu, such as computer skills, but do easily translate into other RPGs, and so they are allowed in those games.) For instance if a player has real world combat experience or investigative capabilities or survival skills and experience, then those things are written into the characters so that the characters become de facto expressions not only of in-game capabilities, but also of real world capabilities. This links character and player closely and gives the players a chance to practice their real skills in-game.
5. Expressive Mechanics - not every capability my players possess has to be expressed mechanically in the game to be able to be utilized. If I have observed capabilities in a person or player that are not accounted for in-game but a particular situation seems to elicit these capabilities, then even if there is no prior or prearranged chatter method of expressing such an ability, I let the player play to the limits of their imagination and resourcefulness. Mechanics don't necessarily limit capabilities nor do lack of mechanics mean the game cannot create a suitable expression ad hoc. This is kind of a nebulous aspect of the game, like a player saying to me, "this doesn't feel right" and so by that observation has shown me that they are particularly alert and suspicious, so they gain an advantage by their acuteness. If they do that all of the time, then they overplay it and it has little or no effect.
6. I encourage expressions of heroism, intelligence, courage, wisdom, morality, etc. not so much as mechanical devices, like wisdom as a function of saving throw, but rather, wisdom as good choice making and being able to see and understand things that are overlooked by others. And to tie those things between player and character. I call that Player Expressionism. That is to say I don't look at intelligence merely as a mechanical means of gaining spell capabilities or charisma as a matter of gaining a +2 on diplomacy, but rather, assuming this world were real, then how would these attributes really function in such a world? Then I try to encourage my players, and I allow my players, to play in that manner. If they show particularly good skills at diplomacy or argument, that is their diplomacy bonus. The way they behaved.
7. Arcane magic, over time, can cause mutations or alterations either in the characters employing magic, or in those within the areas of effect of that magic. Sometimes these alterations are obvious, and sometimes subtle and unnoticed for the most part. But magic has its' price. Divine magic, which in my milieu stems from God is entirely miraculous in nature and therefore not always controllable. A spell might be thrown with the intention of healing a person, and it may do that partially, and also have a completely different effect. Or it may seem to fail entirely and have actually influenced another person or situation that has gone previously unnoticed. Divine magic may have greater and more far reaching consequences than anticipated, or far lesser than hoped. I try not to allow it to become capricious, evening out known and unknown, and good and unlooked for effects, but it is unpredictable at times, more as miracles should be. Arcane magic has secret costs, Divine magic has unpredictable results because God, not the character is the real source and operator of the miracle. Or at other times God and the player are cooperative employers of a miracle, kind of mutual agents towards a common and greater goal. I don't really have terms for those kinds of things, but I guess I should develop some sometime maybe.
8. Into every adventure or mission or scenario I try to work in one or more really big or difficult intentional physical, mental, psychological, spiritual, and moral dilemma. Sometimes these various dilemmas are all related, and sometimes they are all separate in nature, sometimes only a certain type of dilemma appears, at another times all the different types of dilemmas appear. I call this the Operational Dilemma. At times I try to make these dilemmas conflict one with another, so that the spiritual and moral dilemmas might conflict with the physical or psychological dilemma. Then see what the players do about that.
9. I try to encourage player envelopment through the game and through character development. In game this relates to 4, 5, 6, and 8 above. I call this Player-Character Synergy. The point is to establish as close as is possible a linkage between player and character. The player though, in my games, is a far more important consideration than the character. If the player gains and the character loses, that's better than the other way around.
10. We don't employ magic items like Christmas tree ornaments, but over time, certain magic items become "fixed" to the players who employ them. And so they may become modified in function. The same for the way characters use magic and other things. In time experience can lead to either new capabilities or better employment of existing capabilities. That's the Experiential Curve. It's different from "unlocking" because a device might gain an entirely different or unique function over time depending upon the way the player and character interacts with it. Or interacts with others while employing it. Or a player may add to or extract from a device, within reason. This is also related to number 7 above.
11. Invention and Preparation - I encourage all of my players to invent, and to prepare. To think of new uses for old resources, to employ tools and devices in ways never tried before, to prepare for encounters innovatively, to try to develop new skills (both character skills and personal, player skills). To innovate in a wide range of ways.
12. Real World Utility and Problem Solving - We play with a heavy emphasis on real world utility. And on Problem solving. If, for explample, the players intercept a coded communication in Greek or Latin, then they do not "roll for translation" or use a "decode spell" (though they may - but the point is not that the game mechanics do things for you, but rather that through the game, you do things). Instead they translate it for themselves and decode it for themselves. This leads directly to Multi-Tasking. For instance if they intercept a coded communication then while one person is busy translating and working that puzzle the others may continue exploration or working another problem. So the whole group doesn't necessarily stop what they are doing for single action pursuits, unless it is a particularly difficult or dangerous one, but rather people are working different things simultaneously. That is an extremely useful skill for real world situations because in real life the world does not stop rotating merely because you have a translation to make, or some piece of Intel to analyze. Often times you have to juggle and work several different problems more or less simultaneously, or within a given deadline, and so you have to learn to prioritize problems and work more than one thing at a time.
Speaking of which I had in no way intended to spend so much time on this at this moment.
I just had a little extra time cause my partners were late. I'm sure I made plenty of errors though in my haste.
Gotta go. Good luck.