Oh boy do I like threads like this. You asked for it!
Double Action - An active skill that gives the player two moves in a single turn at a heavy stamina/mana/whatever (hereafter referred to as stamina) cost. Probably shouldn't allow this to be used multiple times in a single turn.
Dash - The player gets two/three/however many turns to use all at once in exchange for stamina. The player may only move during these turns, they may not attack or use items or special abilities. If I remember correctly, ToME 4 has abilities like this.
Throw - An attack skill that inflicts damage and and throws the targeted enemy a number of squares in a selected direction based on the player's strength. Maybe allow the player to throw enemies into other enemies? Or inflict extra damage if the thrown enemy strikes a wall? Maybe even allow them to break through the wall if the player's strength is high enough? Some mechanic will need to be in place to ensure that the player can't spam this to avoid all damage in hand to hand combat, such as making most hand to hand fighters harder to throw.
Here's an idea: you've got these equipable magic items, we'll just say rings because every RPG has rings. And these rings can cast a spell like traditional wands do, but instead of recharging from scrolls or waiting or whatever, they recharge when exposed to sunlight. The idea is that you can customize your character with two (or however many) extra abilities from your rings. There's no compulsion to farm until your inventory is full of them, since you can only use two anyway, and there's no reason to rest for hours after every fight because they only recharge outside of the dungeon. The rings would need to lose all of their charges whenever you put them on or take them off to ensure that stockpiling a million of them isn't productive.
Magic Mirror (from
The Water Nixie) - When thrown, this item converts a large area of terrain into perfectly smooth, slippery glass. Moving on this glass takes twice as long. Attacking and defending while standing on glass is also more difficult. You could include a bunch of other items that create other terrain types like magma, or water, or regular floor tiles, or whatever. I think that could open up a lot of possibilities.
What about an extremely powerful item that can resolve almost any encounter, but comes with a permanent consequence? Like, you use it, and for the next 50 turns all of your stats are multiplied by 5, but when it wears off, all of your stats are permanently reduced by 10%. Or maybe it's like Sauron's ring and it gradually corrupts your mind. Or it's a quest item with a limited number of uses, and you can't access certain content or get specific endings or whatever if you use it up. I think there's a lot that could be done with that concept.
If you want to try some uncommon mechanics, I'd like to see more RPGs use perks instead of attribute scores. Like, instead of raising strength so you punch harder and can carry more stuff, you take the punchmaster perk for +1 to punch damage and and weightlifter perk for +20 to inventory capacity. Or maybe you only want the knockout punches, so you take that. Now you've got a second perk available that you can invest in magic or punchmaster 2 or whatever. That kind of things allows for much more character diversity than a traditional attribute system.
Another mechanic I think a lot of RPGs could improve on is conditions. Most RPGs give you a % chance to inflict poison or instant death, and it's almost never balanced, and it's frustrating a lot of the time and I just don't think it's a good system. I dunno if you've ever played Dark Souls, but it takes a really clever approach to conditions. Basically, a 50% poison rate doesn't mean every attack has a 50/50 chance of inflicting poison, it means that, for an enemy with 0% poison resistance, you will inflict poison on the second attack. No dependence on luck, no frustration, and conditions become more useful in general. You can even balance instant death abilities this way - just make stronger enemies and bosses resistant, so it takes a higher number of casts to pull it off.
Another series that handles conditions well is Etrian Odyssey. Conditions in those games are generally really effective, but enemies build up a resistance to them as you use them more. So, say you cast a paralysis spell on a boss enemy and make him miss his turn. Obviously this would be difficult to balance in a traditional RPG system. But in EO, they make it so the first cast of paralysis always hits, and you get a few free turns. You're rewarded for including a dude in your team who can paralyze. After the boss recovers, if you want to paralyze them again, you've got a 50% chance to succeed. So it still might be useful, but it's not a sure thing anymore. If you manage to inflict paralysis again, the third attempt will have a 1 in 4 chance to succeed, and so on. It ensures that conditions are useful while preventing them from trivializing dangerous encounters.
Of the two, I think the Dark Souls system is better, but they both have their merits, and you could probably even combine them if you wanted to.
DDRogue and its kind-of-sequel PrincessRL are also great games to look at if you want unique ideas for equipment and abilities.